We have calculated an array of stellar models for Procyon A that are based on the best physics available to us, including the latest opacities and nuclear cross sections. The array of models spans the error space centered on Procyon's mass, chemical composition, effective temperature, and luminosity. We find that with OPAL opacities no convective overshoot is needed at the edge of the convective core to match Procyon's position in the H-R diagram. We discuss the discrepancy between the astrophysical mass and the astrometric mass, which is reduced by the more up-to-date physics in the models, and describe how oscillation data can be used to distinguish among the possible models and help resolve the discrepancy. We have calculated oscillation frequencies for the l = 0, 1, 2, and 3 p-modes and oscillation periods for the l = 1, 2, and 3 g-modes for several of these models. We also investigate the importance of gravitational settling (i.e., diffusion) of elements in Procyon. Although other evidence, such as recent observations of C, N, and O abundances in F-type disk stars, suggests that diffusion of heavier than Li elements is unlikely to be important (He and Li diffusion are not ruled out), we show how the oscillation modes can be used to independently verify whether or not diffusion is taking place in Procyon (and other stars with thin convective envelopes.