This paper expands on the stochastic version of the strategy-based congested transit assignment problem described in Codina and Rosell (2017b), specifically by extending it to cases dealing with explicit line capacities. Following this previous work, the stochastic model with explicit line capacities takes into account the stochastic mean waiting times and in-vehicle travel times of passengers at stops during the standard scenario journey of the planning period. This slightly modified model is formulated also as a stochastic variational inequality derived from the deterministic version of the problem with similar properties and characteristics, formulated by the authors in a previous work. For this stochastic capacitated model, two algorithms are presented which may take advantage of simplified simulation models for the bus stops in order to provide realistic mean waiting times for passengers at stops. Both algorithms can be easily adapted to the case of the model with non-strict capacities by Codina and Rosell (2017b).