Abstract: An algorithm is presented for controlling two-dimensional motion contact bodies with conforming discretization. Since a kind of special boundary element is utilized in the algorithm, the displacement compatibility and traction equilibrium conditions at nodes can be satisfied simultaneously in arbitrary locations of the contact interface. In addition, a method is also proposed in which the contact boundary location can be moved flexibly on the possible contact boundary. This method is effective to deal with moving and rolling contact problems on a possible larger moving or rolling contact region. Numerical examples show effectiveness of the presented scheme.