A structured mesh consisting of uniform, undistorted or regular shaped elements is easy to generate because it does not conform to the geometry. In order to use such a mesh for analysis, the geometry has to be represented independently of the mesh. To apply essential boundary conditions when nodes are not present on the boundary, the implicit boundary method was developed which uses solution structures constructed using approximate step functions. In this paper, this method is extended to solve 3-D magnetostatics and magnetic force computation problems that typically involve an assembly of parts made of several different materials. Traditional nodal elements are used, with specially constructed solution structures, to represent test and trial functions such that both boundary and interface conditions are enforced. Several magnetostatic problems with known solutions are modeled to validate the method.