The influence of interface donor and acceptor traps on the static and dynamic behavior of Ge/Si separate absorption, charge, and multiplication avalanche photodiodes (APDs) is modeled. The effects of different trap types, densities, and carrier capture cross sections on the dark current level, breakdown voltage, dc gain, and electric field profile, as well as on the frequency response and gain-bandwidth product of the device, are investigated for the first time. Our results show that the interface traps significantly increase the dark current and reduce the gain from 290 to less than 10. We also show that the acceptor traps reduce the APD bandwidth considerably to 0.5 GHz whereas the donor traps increase the bandwidth to around 10 GHz.