This study concerns the development of a threedimensional boundary element analysis method for determining the stresses in an elastic domain composed of dissimilar materials with a surface crack perpendicular to the interface. The continuity of displacement and traction components is enforced directly along the interface between the dissimilar material regions of the domain. The presence of material and geometric discontinuities are included in the formulation explicitly. The unknown interface traction components are expressed in terms of the unknown interface displacement components by using the boundary element method for each material region of the domain. Enforcing the continuity conditions leads to a final system of equations containing unknown interface displacement components only. With the solution of interface displacement components, each region has a complete set of boundary conditions, thus leading to the solution of the remaining unknown boundary quantities. The method is demonstrated by solving for the singular stress field and evaluating the fracture parameters for a surface crack perpendicular to the interface between a thin-film and a substrate.