In this research, we study numerical methods for interest rate derivatives under several models. We consider pricing American put options on zero-coupon bonds under a single factor model of short-term rate, and valuing caps under Lognormal Forward-LIBOR Model (LFM). Monte Carlo method and a novel PDE method are illustrated for pricing caps under one-factor and two-factor LFM. Also, the performance of different models for pricing interest rate derivatives is compared.