Transit assignment models are particularly useful to systematically access the operation or planning of a transit network. From this perspective, the transit assignment model has been developed and applied for a long time, and various of formulations come out to fulfill different application purposes. In order to analyze the uncertainties in transit network which may be caused by probabilistic travel demand, congestion effect, or transit frequencies, a variational inequality (VI) formulation is employed in this study. It models the passengers' route choice subject to congestion from waiting and in-vehicle time. The hyperpath concept is used to incorporate the passengers' strategy at transit stops. Then, the analytical sensitivity analysis expression is derived for the transit assignment model. Some typical applications of sensitivity analysis results will be discussed in numerical example. Especially, the uncertainties from the travel demand are considered as the random variables with mean and variance. Based on the analytical sensitivity analysis, the uncertainties in the result of transit assignment model will be estimated.