Delete a row in Excel VBA

Chris Nielsen's solution is simple and will work well. A slightly shorter option would be...

ws.Rows(Rand).Delete

...note there is no need to specify a Shift when deleting a row as, by definition, it's not possible to shift left

Incidentally, my preferred method for deleting rows is to use...

ws.Rows(Rand) = ""

...in the initial loop. I then use a Sort function to push these rows to the bottom of the data. The main reason for this is because deleting single rows can be a very slow procedure (if you are deleting >100). It also ensures nothing gets missed as per Robert Ilbrink's comment

You can learn the code for sorting by recording a macro and reducing the code as demonstrated in this expert Excel video. I have a suspicion that the neatest method (Range("A1:Z10").Sort Key1:=Range("A1"), Order1:=xlSortAscending/Descending, Header:=xlYes/No) can only be discovered on pre-2007 versions of Excel...but you can always reduce the 2007/2010 equivalent code

Couple more points...if your list is not already sorted by a column and you wish to retain the order, you can stick the row number 'Rand' in a spare column to the right of each row as you loop through. You would then sort by that comment and eliminate it

If your data rows contain formatting, you may wish to find the end of the new data range and delete the rows that you cleared earlier. That's to keep the file size down. Note that a single large delete at the end of the procedure will not impair your code's performance in the same way that deleting single rows does

Change your line

ws.Range(Rand, 1).EntireRow.Delete

to

ws.Cells(Rand, 1).EntireRow.Delete 

Better yet, use union to grab all the rows you want to delete, then delete them all at once. The rows need not be continuous.

dim rng as range
dim rDel as range

for each rng in {the range you're searching}
   if {Conditions to be met} = true then
      if not rDel is nothing then
         set rDel = union(rng,rDel)
      else
         set rDel = rng
      end if
   end if
 next
 
 rDel.entirerow.delete

That way you don't have to worry about sorting or things being at the bottom.