Abstract: Based on the previous investigation on 2D moving and rolling contact problem by BEM, the conforming discretization is generalized to 3D cases. A scheme of boundary element method for moving contact of 3D elastic solids with prescribed moving direction using conforming discretization is presented. Both the displacement and traction boundary conditions are satisfied on the contacted region in the sense of discretization. In this way the good characteristics of BEM is preserved. The possible contact surface of each body is divided into special right triangle elements with the same size along the moving direction. Each element of triangular shape has three fixed nodes at the corners of the triangular element, and three movable nodes on each side of the element. The location of the movable nodes on a boundary element of one contacted solid is determined by the fixed nodes and their connection lines of another corresponding contacted solid. At each instant of the moving contact, the element is divided into 4 triangle sub-elements, on which the displacements and tractions are linearly interpolated. Some numerical examples are given to show the effectiveness and the higher accuracy of the schemes.