Magnetostatic field problems are solved in three dimensions by applying a variational method that employs finite elements. Formulation through a partial differential equation allows solution for the magnetic vector potential given an inhomogeneous, orthotropic medium and a distributed current source. Three vector boundary conditions are discussed and interior sheet currents are allowed within the medium. In addition, the Lorentz condition is enforced by including a penalty term in the energy functional. A point-iterative algorithm is used to solve the set of equations resulting from finite element discretization. This method is particularily suitable for regions with regular geometry and a moderate (1,000 to 10,000) number of unknowns.