To some extent, yes.
if you run the analysis twice with the same mesh, you shouldn't get different answers but there is a possibility of rounding....etc being done slightly differently.
if you run the same analysis and it has been meshed before each run, you could get slightly different answers because there isn't a guarantee that the mesh will be exactly the same.
what is the issue you are running into?
and just to add another comment, i'd recommend looking at displacement, not stress first. also look in several places, not just the max if you're trying to compare solutions.