这是一个正确的解决办法。无论一周的第一天是周一、周日还是其他日期，下面的代码都能正常工作。

public static class DateTimeExtension
{
  public static DateTime GetFirstDayOfThisWeek(this DateTime d)
  {
    CultureInfo ci = System.Threading.Thread.CurrentThread.CurrentCulture;
    var first = (int)ci.DateTimeFormat.FirstDayOfWeek;
    var current = (int)d.DayOfWeek;

    var result = first <= current ?
      d.AddDays(-1 * (current - first)) :
      d.AddDays(first - current - 7);

    return result;
  }
}

class Program
{
  static void Main()
  {
    System.Threading.Thread.CurrentThread.CurrentCulture = CultureInfo.GetCultureInfo("en-US");
    Console.WriteLine("Current culture set to en-US");
    RunTests();
    Console.WriteLine();
    System.Threading.Thread.CurrentThread.CurrentCulture = CultureInfo.GetCultureInfo("da-DK");
    Console.WriteLine("Current culture set to da-DK");
    RunTests();
    Console.ReadLine();
  }

  static void RunTests()
  {
    Console.WriteLine("Today {1}: {0}", DateTime.Today.Date.GetFirstDayOfThisWeek(), DateTime.Today.Date.ToString("yyyy-MM-dd"));
    Console.WriteLine("Saturday 2013-03-02: {0}", new DateTime(2013, 3, 2).GetFirstDayOfThisWeek());
    Console.WriteLine("Sunday 2013-03-03: {0}", new DateTime(2013, 3, 3).GetFirstDayOfThisWeek());
    Console.WriteLine("Monday 2013-03-04: {0}", new DateTime(2013, 3, 4).GetFirstDayOfThisWeek());
  }
}

这将返回一周的开始和结束日期:

    private string[] GetWeekRange(DateTime dateToCheck)
    {
        string[] result = new string[2];
        TimeSpan duration = new TimeSpan(0, 0, 0, 0); //One day 
        DateTime dateRangeBegin = dateToCheck;
        DateTime dateRangeEnd = DateTime.Today.Add(duration);

        dateRangeBegin = dateToCheck.AddDays(-(int)dateToCheck.DayOfWeek);
        dateRangeEnd = dateToCheck.AddDays(6 - (int)dateToCheck.DayOfWeek);

        result[0] = dateRangeBegin.Date.ToString();
        result[1] = dateRangeEnd.Date.ToString();
        return result;

    }

我已经在我的博客上发布了计算周、月、季度和年的开始/结束的完整代码 ZamirsBlog

这是一个正确的解决办法。无论一周的第一天是周一、周日还是其他日期，下面的代码都能正常工作。

public static class DateTimeExtension
{
  public static DateTime GetFirstDayOfThisWeek(this DateTime d)
  {
    CultureInfo ci = System.Threading.Thread.CurrentThread.CurrentCulture;
    var first = (int)ci.DateTimeFormat.FirstDayOfWeek;
    var current = (int)d.DayOfWeek;

    var result = first <= current ?
      d.AddDays(-1 * (current - first)) :
      d.AddDays(first - current - 7);

    return result;
  }
}

class Program
{
  static void Main()
  {
    System.Threading.Thread.CurrentThread.CurrentCulture = CultureInfo.GetCultureInfo("en-US");
    Console.WriteLine("Current culture set to en-US");
    RunTests();
    Console.WriteLine();
    System.Threading.Thread.CurrentThread.CurrentCulture = CultureInfo.GetCultureInfo("da-DK");
    Console.WriteLine("Current culture set to da-DK");
    RunTests();
    Console.ReadLine();
  }

  static void RunTests()
  {
    Console.WriteLine("Today {1}: {0}", DateTime.Today.Date.GetFirstDayOfThisWeek(), DateTime.Today.Date.ToString("yyyy-MM-dd"));
    Console.WriteLine("Saturday 2013-03-02: {0}", new DateTime(2013, 3, 2).GetFirstDayOfThisWeek());
    Console.WriteLine("Sunday 2013-03-03: {0}", new DateTime(2013, 3, 3).GetFirstDayOfThisWeek());
    Console.WriteLine("Monday 2013-03-04: {0}", new DateTime(2013, 3, 4).GetFirstDayOfThisWeek());
  }
}

public static System.DateTime getstartweek()
{
    System.DateTime dt = System.DateTime.Now;
    System.DayOfWeek dmon = System.DayOfWeek.Monday;
    int span = dt.DayOfWeek - dmon;
    dt = dt.AddDays(-span);
    return dt;
}

把这些都放在一起，加上全球化并允许指定一周的第一天作为我们通话的一部分

public static DateTime StartOfWeek ( this DateTime dt, DayOfWeek? firstDayOfWeek )
{
    DayOfWeek fdow;

    if ( firstDayOfWeek.HasValue  )
    {
        fdow = firstDayOfWeek.Value;
    }
    else
    {
        System.Globalization.CultureInfo ci = System.Threading.Thread.CurrentThread.CurrentCulture;
        fdow = ci.DateTimeFormat.FirstDayOfWeek;
    }

    int diff = dt.DayOfWeek - fdow;

    if ( diff < 0 )
    {
        diff += 7;
    }

    return dt.AddDays( -1 * diff ).Date;

}

以下是一些答案的组合。它使用一个扩展方法，允许传入区域性。如果没有传入，则使用当前区域性。这将为它提供最大的灵活性和重用性。

/// <summary>
/// Gets the date of the first day of the week for the date.
/// </summary>
/// <param name="date">The date to be used</param>
/// <param name="cultureInfo">If none is provided, the current culture is used</param>
/// <returns>The date of the beggining of the week based on the culture specifed</returns>
public static DateTime StartOfWeek(this DateTime date, CultureInfo cultureInfo=null) =>
    date.AddDays(-1 * (7 + (date.DayOfWeek - (cultureInfo ?? CultureInfo.CurrentCulture).DateTimeFormat.FirstDayOfWeek)) % 7).Date;

使用示例:

public static void TestFirstDayOfWeekExtension() {
    DateTime date = DateTime.Now;
    foreach(System.Globalization.CultureInfo culture in CultureInfo.GetCultures(CultureTypes.UserCustomCulture | CultureTypes.SpecificCultures)) {
        Console.WriteLine($"{culture.EnglishName}: {date.ToShortDateString()} First Day of week: {date.StartOfWeek(culture).ToShortDateString()}");
    }
}