A spatial finite element method is formulated for neutron transport calculations in two-dimensional reactor lattice cells in x-y geometry. The method is closely related to classical integral transport techniques in that scalar flux equations result that are similar in form to those of collision probability methods. The use of triangular spatial elements permits flexible geometrical representation of material regions, including regions with curved interfaces. On a rectangular domain, a block inversion technique provides for the incorporation of exact-reflected boundary conditions into the transport kernel. The method is implemented in a computer code and illustrated in a series of lattice cell calculations.