Processes of contact interaction between elements of wedge free-wheel mechanisms are studied as part of a planar static problem of the elasticity theory at the stage of the active application of a load. A nonconservative model of the mechanism is developed that, unlike the continual model, takes into account the presence of Coulomb friction on the working surfaces of contacting elements. A technique for the numerical implementation of the problem by the boundary-element method and an iteration algorithm are developed that enable simulation of the behavior of wedge mechanisms at the stage of wedging and in a wedged state. Solutions of the contact problem are found in a broad range of variations of computational parameters and for different histories of loading of the mechanism.