只使用:

ViewController *viewController = [[ViewController alloc] init];

UINavigationController *navController = [[UINavigationController alloc] initWithRootViewController:viewController];
navController.navigationBarHidden = YES;

[self presentViewController:navController animated:YES completion: nil];
[viewController release];
[navController release];

虽然这里所有的答案都很棒，而且大多数工作得很好，但有一个稍微简单一点的方法可以达到同样的效果……

推动:

  NextViewController *nextViewController = [[NextViewController alloc] init];

  // Shift the view to take the status bar into account 
  CGRect frame = nextViewController.view.frame;
  frame.origin.y -= 20;
  frame.size.height += 20;
  nextViewController.view.frame = frame;

  [UIView transitionFromView:self.navigationController.topViewController.view toView:nextViewController.view duration:0.5 options:UIViewAnimationOptionTransitionFlipFromRight completion:^(BOOL finished) {
    [self.navigationController pushViewController:nextViewController animated:NO];
  }];

流行:

  int numViewControllers = self.navigationController.viewControllers.count;
  UIView *nextView = [[self.navigationController.viewControllers objectAtIndex:numViewControllers - 2] view];

  [UIView transitionFromView:self.navigationController.topViewController.view toView:nextView duration:0.5 options:UIViewAnimationOptionTransitionFlipFromLeft completion:^(BOOL finished) {
    [self.navigationController popViewControllerAnimated:NO];
  }];}

从示例应用程序中，可以看到这种变化。 https://github.com/mpospese/MPFoldTransition/

#pragma mark - UINavigationController(MPFoldTransition)

@implementation UINavigationController(MPFoldTransition)

//- (void)pushViewController:(UIViewController *)viewController animated:(BOOL)animated
- (void)pushViewController:(UIViewController *)viewController foldStyle:(MPFoldStyle)style
{
    [MPFoldTransition transitionFromViewController:[self visibleViewController] 
                                  toViewController:viewController 
                                          duration:[MPFoldTransition defaultDuration]  
                                             style:style 
                                        completion:^(BOOL finished) {
                                            [self pushViewController:viewController animated:NO];
                                        }
     ];
}

- (UIViewController *)popViewControllerWithFoldStyle:(MPFoldStyle)style
{
    UIViewController *toController = [[self viewControllers] objectAtIndex:[[self viewControllers] count] - 2];

    [MPFoldTransition transitionFromViewController:[self visibleViewController] 
                                  toViewController:toController 
                                          duration:[MPFoldTransition defaultDuration] 
                                             style:style
                                        completion:^(BOOL finished) {
                                            [self popViewControllerAnimated:NO];
                                        }
     ];

    return toController;
}

基于jordanperry为swift 4更新的答案

用于推送UIViewController

let yourVC = self.storyboard?.instantiateViewController(withIdentifier: "yourViewController") as! yourViewController
    UIView.animate(withDuration: 0.75, animations: {() -> Void in
    UIView.setAnimationCurve(.easeInOut)
    self.navigationController?.pushViewController(terms, animated: true)
    UIView.setAnimationTransition(.flipFromRight, for: (self.navigationController?.view)!, cache: false)
})

为流行

UIView.animate(withDuration: 0.75, animations: {() -> Void in
    UIView.setAnimationCurve(.easeInOut)
    UIView.setAnimationTransition(.flipFromLeft, for: (self.navigationController?.view)!, cache: false)
})
navigationController?.popViewController(animated: false)

@Luca Davanzo的答案在Swift 4.2

public extension UINavigationController {

    /**
     Pop current view controller to previous view controller.

     - parameter type:     transition animation type.
     - parameter duration: transition animation duration.
     */
    func pop(transitionType type: CATransitionType = .fade, duration: CFTimeInterval = 0.3) {
        self.addTransition(transitionType: type, duration: duration)
        self.popViewController(animated: false)
    }

    /**
     Push a new view controller on the view controllers's stack.

     - parameter vc:       view controller to push.
     - parameter type:     transition animation type.
     - parameter duration: transition animation duration.
     */
    func push(viewController vc: UIViewController, transitionType type: CATransitionType = .fade, duration: CFTimeInterval = 0.3) {
        self.addTransition(transitionType: type, duration: duration)
        self.pushViewController(vc, animated: false)
    }

    private func addTransition(transitionType type: CATransitionType = .fade, duration: CFTimeInterval = 0.3) {
        let transition = CATransition()
        transition.duration = duration
        transition.timingFunction = CAMediaTimingFunction(name: CAMediaTimingFunctionName.easeInEaseOut)
        transition.type = type
        self.view.layer.add(transition, forKey: nil)
    }

}

意识到这是一个老问题。我仍然想张贴这个答案，因为我有一些问题弹出几个viewcontroller与建议的答案。我的解决方案是子类UINavigationController和覆盖所有的弹出和推方法。

翻转导航控制器.h

@interface FlippingNavigationController : UINavigationController

@end

FlippingNavigationController.m：

#import "FlippingNavigationController.h"

#define FLIP_DURATION 0.5

@implementation FlippingNavigationController

- (void)pushViewController:(UIViewController *)viewController animated:(BOOL)animated
{
    [UIView transitionWithView:self.view
                      duration:animated?FLIP_DURATION:0
                       options:UIViewAnimationOptionCurveEaseInOut | UIViewAnimationOptionTransitionFlipFromRight
                    animations:^{ [super pushViewController:viewController
                                                   animated:NO]; }
                    completion:nil];
}

- (UIViewController *)popViewControllerAnimated:(BOOL)animated
{
    return [[self popToViewController:[self.viewControllers[self.viewControllers.count - 2]]
                             animated:animated] lastObject];
}

- (NSArray *)popToRootViewControllerAnimated:(BOOL)animated
{
    return [self popToViewController:[self.viewControllers firstObject]
                            animated:animated];
}

- (NSArray *)popToViewController:(UIViewController *)viewController animated:(BOOL)animated
{
    __block NSArray* viewControllers = nil;

    [UIView transitionWithView:self.view
                      duration:animated?FLIP_DURATION:0
                       options:UIViewAnimationOptionCurveEaseInOut | UIViewAnimationOptionTransitionFlipFromLeft
                    animations:^{ viewControllers = [super popToViewController:viewController animated:NO]; }
                    completion:nil];

    return viewControllers;
}

@end