The evolution of circulating viruses is shaped by their need to evade antibody response, which mainly targets the viral spike. Because of the high density of spikes on the viral surface, not all antigenic sites are targeted equally by antibodies. We offer here a geometry-based approach to predict and rank the probability of surface residues of SARS spike (S protein) and influenza H1N1 spike (hemagglutinin) to acquire antibody-escaping mutations utilizing in-silico models of viral structure. We used coarse-grained MD simulations to estimate the on-rate (targeting) of an antibody model to surface residues of the spike protein. Analyzing publicly available sequences, we found that spike surface sequence diversity of the pre-pandemic seasonal influenza H1N1 and the sarbecovirus subgenus highly correlates with our model prediction of antibody targeting. In particular, we identified an antibody-targeting gradient, which matches a mutability gradient along the main axis of the spike. This identifies the role of viral surface geometry in shaping the evolution of circulating viruses. For the 2009 H1N1 and SARS-CoV-2 pandemics, a mutability gradient along the main axis of the spike was not observed. Our model further allowed us to identify key residues of the SARS-CoV-2 spike at which antibody escape mutations have now occurred. Therefore, it can inform of the likely functional role of observed mutations and predict at which residues antibody-escaping mutation might arise.