Numerical simulations of the interacting galaxies in the NGC 520/UGC 957 system are presented. Two sets of models were produced to investigate the postulated three-galaxy system of two colliding disk galaxies within NGC 520 and the dwarf galaxy UGC 957. The morphology and kinematics of the models are compared with previously obtained optical, infrared, and 21 cm imaging and spectroscopy to choose best-fitting simulations. The first set of models simulated a dwarf perturbing one-disk galaxy, which tested the possibility that NGC 520 contains only one galaxy disturbed by the passage of UGC 957. The resulting morphology of the perturbed single disk in the simulation fails to reproduce the observed tidal tails and northwest mass condensation of NGC 520. A second set of models simulated two colliding disks, which tested the hypothesis that NGC 520 itself contains two galaxies in a strong collision and UGC 957 is unimportant to the interaction. These disk-disk models produced a good match to the morphology of the present NGC 520. A detailed match of the internal kinematics could not be reached, at least partly due to the restrictions of the modeling technique. Also, the southern tidal in the disk-disk simulation was too short. We conclude that (1) NGC 520 contains two colliding disk galaxies which have produced the brighter southern half of the long tidal tail and (2) UGC 957, which may originally have been a satellite of one of the disk galaxies, formed the diffuse northern tail as it orbited NGC 520. The time scale for the collision of the two disks is approximately 3 x 10(8) years. Implications of the disks' collision for their gas components and the apparently enhanced star formation rate are discussed.