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The variational nodal method is generalized to include R-Z geometry. Spherical harmonic trial functions in angle are combined with orthonormal polynomials in space to discretize the multigroup equations. The nodal response matrices that result correspond to volumes that are toroids, with rectangular cross sections, except along the centerline where the volumes are cylinders. The R-Z response matrix equations are implemented as modifications to the Argonne National Laboratory code VARIANT, and existing iterative methods are used to obtain numerical solutions. The method is tested in P₁, P₃, and P₅ approximations, and results are presented for both a one-group fixed source and a two-group eigenvalue problem.