The concept of a model that solves the transit equilibrium assignment problem for large scale transit networks and a computational system are developed. The First Principle of Equilibrium of Wardrop, also known as equilibrium user optimum, is applied in this work. A model with static equilibrium and fixed demand is considered. The equilibrium flow can be attained by solving a non- linear minimization problem that includes objective function non-linear and linear constraints. An adaptation of Frank-Wolfe algorithm (efficient to solve transportation stochastic problems) and a logit assignment model are used to solve the problem. This metodology is applied to a network of the Metropolitan Region of Rio de Janeiro.