In this paper, an approach to numerical integration of equations governing motion of con- strained mechanical systems is suggested. In this approach, unknown reaction forces acting on the sys- tem are treated as controls, and the algebraic equations that these reactions satisfy, as control goals. Based on the suggested approach, an algorithm for numerical solving rolling equations is developed. The discussion is illustrated by the example of application of the algorithm to solve the problem of a heavy wheel rolling along a curvilinear profile without slippage.