BYPASSR uses a Bayesian MCMC method that allows very complex substitution models to be implemented, including models in which the substitution rate varies continuously across sites. The novel aspect of our technique is the use of uniformization of the Markov substitution process to integrate over substitution events along the branches of a phylogeny without specifying the particular transitions that occurred on a branch. An advantage of this formulation of the transition probabilities is that it allows efficient augmentation of the data in a MCMC analysis by treating the substitution events as random variables in the chain and eliminating the need to numerically calculate the transition probabilities in complex substitution models by use of matrix exponentiation. The method is evaluated by using simulated data to examine the accuracy of inferred site-specific rates and branch lengths under a simple substitution model with gamma distributed rate variation. The performance is compared to that of existing methods implemented in the program PAML. The method can be readily implemented for use with much more complex substitution models and has the potential to greatly simplify estimation of site-specific rates under such models.