This paper demonstrates the application of Bayesian simulation-based estimation to a class of interest rate models known as Affine Term Structure (ATS) models. The technique used is based on a Markov Chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time model using discretely observed data. The technique is demon-strated using a one-factor ATS model, with the latent factor process that underlies the yields sampled via a single-move algorithm. Numerical application of the method is demonstrated using both simulated and empirical data. Extension of the method to a three-factor ATS model is also discussed, as well as the application of a multi-move sampler based on a Kalman Filtering and Smoothing algorithm.Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation, Nonlinear State Space Models, Kalman Filtering.