If it is Monday, Saturday or Sunday then get last Friday's date

This works:

Set Datefirst = 6  -- Set 'first day of week' to Saturday

Select @DayWk = Datepart(dw, getdate())    -- Get day of week, with Sat=1, Sun=2, etc.

If @DayWk <= 3   -- If Sat, Sun, Mon
   Select Dateadd(d, -(@DayWk), Cast(Convert(varchar, getdate(), 112) as datetime)) As LastWorkDay  -- Subtract that day value from the current day
Else
   Select Dateadd(d, -1, Cast(Convert(varchar, getdate(), 112) as datetime)) As LastWorkDay   -- subtract 1 from the current day

Set Datefirst = 7  -- set back to normal

I didn't see the "yesterday's date" part, because the Asker JUST asked almost the exact same question here:  http:/Q_20849690.html  ... Weird.  

Anyway, here is my updated answer:
     DECLARE @DayWk DATETIME

     SET @DayWk = DATEADD( d, CASE DATEPART(dw,GETDATE())
                         WHEN 1 THEN -2
                         WHEN 2 THEN -3
                         ELSE -1
                    END, @dt)

Dex*

Good point:  Looking at your code, I can simplify mine down to:

Select Dateadd(d, -(1 + CASE WHEN Datepart(dw, getdate()) <=2 Then Datepart(dw, Getdate()) Else 0 END), Cast(Convert(varchar, getdate(), 112) as datetime)) As LastWorkDay

@MuscleJack : Why would you accept an answer that doesn't even work?

If anything, you should use this:
     Select  @DayWk     =
     case
       when datepart(dw, GETDATE()) = 1 then dateadd(dd, -2, GETDATE())
       when datepart(dw, GETDATE()) = 2 then dateadd(dd, -3, GETDATE())
       when datepart(dw, GETDATE()) = 7 then dateadd(dd, -1, GETDATE())
       else dateadd(dd, -1, GETDATE())
     end

It wasn't first, it is correct, and it isn't even the best one.  Would you please explain why you chose it?

Dex*

the best solution is to do the following:

SET DATEFIRST 5;
-- Set it to the friday

select distinct dateadd(day,(datepart(weekday,getDate())*-1)+1,getdate())  

Here's the logic - We base the date index as of friday.
Then we see how far away are we from friday - datepart(weekday,getDate()) will give us that.
We just need to subtract these many numbers of days from the present date to get the last friday.
So multiply it by -1, and use the DateAdd function to add these two.

vjammy's solution is arguably the most efficient, elegant and simple to implement.

dmeenan,
I am not sure if you realized, but this question was closed over 5 years ago.

>>vjammy's solution is arguably the most efficient, elegant and simple to implement.<<
That may be the case, but I just tested it and I get last Friday Oct 30.  But today is Wednesday, so I think it is fair to say that is not what the author desired:
"If it is Monday, Saturday or Sunday then get last Friday's date else get yesterday's date"