For proteins to function, they must first fold and then bind appropriate partners in stable ways. Failure to do either of these will usually be lethal. Molecular modeling provides a way to predict the effects of many potential mutations on folding and binding stability—and thereby, a way to predict mutational viability of future viruses. To test this concept, we studied mutations in the coat protein of the Microvirid bacteriophage φX174. We engineered all possible variants at 21 sites of the protein’s 176 residues, determined the viability of each, and tested the ability of molecular modeling to predict viability. We found that just over half of the variants are viable (223 of 420, or 53%). We developed a new type of logistic-regression model to assess how well predicted stability effects (ΔΔG) explain phage viability. The model is novel in that it assumes predictors interact multiplicatively (rather than additively) and that the logistic function asymptotes at a value below one. The logistic model indicates viability drops quickly as mutations exceed ΔΔG of +4 kCal/mol. However, we also find that that molecular modeling has only a moderate capacity to predict viability in this phage protein: mutations predicted to be highly destabilizing are indeed inviable, but most mutations are predicted to have small stability effects, and nearly half of these are still inviable. Our results support the view that there are many ways for protein to be non-functional: being unstable is just one of them. Finally, we compare the predictive power of molecular modeling with phylogenic conservation as a different source of information about viability.