The complexity of modeling friction between rough surfaces has prompted many researchers to use Greenwood and Tripp’s sum surface assumption to simplify the analysis. This assumption approximates the contact between two rough surfaces as contact between their equivalent sum surface and a rigid plane. In this work, we develop detailed finite element models to test the sum surface assumption for surfaces with Gaussian and exponential autocorrelation functions. We consider surfaces with differing surface roughness and correlation length values. For each case, we conduct simulations of two rough surfaces interacting in compression followed by shear, and a corresponding equivalent surface model based on the sum surface assumption. Multiple realizations of each parameter combination are simulated to obtain a statistical picture of the responses. We find that (a) the sum surface assumption consistently under-predicts the static coefficient of friction and (b) the equivalent surface model is less accurate for surfaces with differing correlation length-to-surface roughness ratios.