In this article, a novel numerical algorithm to simulate power transient in backward pumped Raman amplifiers is proposed. Based on this algorithm, transient response to a slowly varying input power waveform is investigated for the first time. We find that a properly designed, slowly varied input leading edge can reduce the output up-shoot drastically in a single-channel condition, while in a multi-channel condition, a gradually changed input waveform can eliminate the abrupt power up-shoot due to forward signal-to-signal Raman interactions and obtain a better gain clamping result by using pump adjustment. These conclusions will play a role in Raman amplified optical burst mode switching (or packet switching) systems and DWDM networks.