According to the "experimenter's regress", disputes about the validity of experimental results cannot be closed by objective facts because no conclusive criteria other than the outcome of the experiment itself exist for deciding whether the experimental apparatus was functioning properly or not. Given the frequent characterization of simulations as "computer experiments", one might worry that an analogous regress arises for computer simulations. The present paper analyzes the most likely scenarios where one might expect such a "simulationist's regress" to surface, and, (...) in doing so, discusses analogies and disanalogies between simulation and experimentation. I conclude that, on a properly broadened understanding of robustness, the practice of simulating mathematical models can be seen to have sufficient internal structure to avoid any special susceptibility to regress-like situations. (shrink)