The paper presents a nonlinear programming algorithm for the numerical solution of optimal control problem with phase constraints. The direct transcription method is used to transform the initial continuous problem into one of nonlinear programming, characterized by matrices that are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied. The presented algorithm exploits the matrix sparsity and other properties of the problem as well. Computational results are also described to demonstrate both speed and reliability of the proposed method.