A new two-dimensional coarse mesh technique for neutron transport calculations, the constrained finite element method, is formulated and applied to a series of nonuniform lattice problems. Finite elements in space and in angle are applied to the variational form of the even-parity transport equation. Spatial and angular constraints on the finite element trial functions along the intercell boundaries lead to a two-step solution procedure in which a global calculation yields the scalar flux values at coarse mesh nodes located on the intercell boundaries. The flux distributions and reaction rates within each cell are then found in terms of the nodal scalar flux values on the cell boundaries. The method is applied to a series of one-group fixed-source lattice problems, and the results are compared to those obtained from unconstrained finite element reference solutions and/or from response matrix solutions.