Summary: The problem of determining the slow motion of a particle of arbitrary shape near a plane wall in a viscous fluid is formulated exactly as a system of linear Fredholm integral equations of the second kind by completing the deficient range of a double-layer potential and using the adequate image system needed to satisfy the nonslip boundary condition at the plane wall. It is shown that this system of integral equations possesses a unique continuous solution when the boundary of the particle is a Lyapunov surface and the velocity data on the boundary surface is continuous, and this system is used as the basis of a numerical model that uses standard boundary element techniques.