The two-dimensional (2D) gain profiles of InP/InGaAs separate absorption, grading, charge, and multiplication (SAGCM) avalanche photodiodes (APDs) have been modeled by using a simplified stochastic approach. The influence of the curved diffusion edge on the electric field ill the periphery has been considered and electric field equations have been derived from the cylindrical Poisson's equation. The electric field in the multiplication layer is significantly reduced when a partial charge sheet is incorporated in the device's periphery. The modeled 2D gain profile for such a device agrees with experiment and demonstrates an effective suppression of the premature edge breakdown. These results and the uniformity issue of the 2D gain profiles are further discussed. From our analyses, we find that controlling the diffusion process within the p(+) InP top layer and patterning the charge sheet mesa structure are most likely to affect the uniformity and symmetry of the 2D gain profiles for the InP/InGaAs SAGCM ASDs.