The behavior of silicon-based avalanche photodiodes (APD's) operated in the charge storage mode is examined. In the charge storage mode, the diodes are periodically biased to a sub-breakdown voltage and then open-circuited. During this integration period, photo-excited and thermally generated carriers are accumulated within the structure. The dynamics of this accumulation and its effects upon the avalanching of the diode warrants a detailed, fully numerical analysis. The salient features of this investigation include device sensitivity to the input photo-current including the self-quenching effect of the diode and its limitations in sensing low light levels, the dependence of the response on the bulk lifetime and hence on the generation current within the device, the initial gain, transient response, dependence of the device uniformity upon performance, and the quantity of storable charge within the device. To achieve these tasks our device simulator, STEBS-2D, was utilized. A modified current-controlled boundary condition is employed which allows for the simulation of the isolated diode after the initial reset bias has been applied. With this boundary condition, it is possible to establish a steady-state voltage on the ohmic contact and then effectively remove the device from the external circuit while still including effects from surface recombination, trapped surface charge, and leakage current from the read-out electronics.