I am trying use FluentValidation validaton when dropdownlist value is yes and the field must be date. it is working when dropdownlist is yes checking for date. But
also showing validation when I select No still it says Must be date. 
It should not validate anymore if dropdownlist value otherthan the yes. How can we do that?
 RuleFor(x => x.DtPublishedTimeText)
            .NotEmpty()
            .When(HasMaterialPublishedElseWhereText)
            .WithMessage("Required Field")
            .Must(BeAValidDate)
            .WithMessage("Must be date");
private bool BeAValidDate(string val)
{
    DateTime date;
    return  DateTime.TryParse(val, out date);
}
private bool HasMaterialPublishedElseWhereText(MeetingAbstract model)
{
    return model.HasMaterialPublishedElseWhereText != null && 
             model.HasMaterialPublishedElseWhereText.Equals("yes");
}
The issue you are having is the When predicate only applies to one rule. You need to have conditional validation on both the NotEmpty AND  the Must.
There two ways to achieve this. Option 1 is tidier when there are only a couple of conditional rules, otherwise I'd use option 2.
RuleFor(x => x.DtPublishedTimeText)
    .NotEmpty()
        .When(HasMaterialPublishedElseWhereText)
        .WithMessage("Required Field")
    .Must(BeAValidDate)
        .When(HasMaterialPublishedElseWhereText)
        .WithMessage("Must be date");
Or
When(HasMaterialPublishedElseWhereText, () => {
    RuleFor(x => x.DtPublishedTimeText)
        .NotEmpty()
            .WithMessage("Required Field");
    RuleFor(x => x.DtPublishedTimeText)
        .Must(BeAValidDate)
            .WithMessage("Must be date");
});
Do note: I have no idea what HasMaterialPublishedElseWhereText is or what it looks like. I am assuming you can use it as a predicate
EDIT:
I'd also look at refactoring the HasMaterialPublishedElseWhereText method, the following is less error prone.
private bool HasMaterialPublishedElseWhereText(MeetingAbstract model)
{
    return String.Equals(model.HasMaterialPublishedElseWhereText, "yes", StringComparison.InvariantCultureIgnoreCase);
}
You just need to change the order of your calls. Try this:
RuleFor(x => x.DtPublishedTimeText)
    .NotEmpty()
        .WithMessage("Required Field")
    .Must(BeAValidDate)
        .WithMessage("Must be date")
    .When(HasMaterialPublishedElseWhereText);
The When applies to all previous rules. So in your code when you applied it straight after the NotEmpty, it applied only to the NotEmpty rule and not to the Must rule.
Full demo on DotNetFiddle.
Tested in VERSION >= 8.4.0
a new enum parameter is added to When extension method
public enum ApplyConditionTo
{
    //
    // Summary: (default)
    //     Applies the condition to all validators declared so far in the chain.
    AllValidators = 0,
    //
    // Summary:
    //     Applies the condition to the current validator only.
    CurrentValidator = 1
}
by default (AllValidators): When will ending by rules chain ends 
(CurrentValidator): When will be restricted to the first previous rule
来源:https://stackoverflow.com/questions/24024896/fluentvalidation-for-when-must