The symmetric successive overrelaxation (SSOR) method and the symmetric strongly implicit procedure (SSIP) method are applied to a number of two-dimensional elliptic partial differential equations typical of those encountered in reactor engineering. The SSIP method is then incorporated in a program for multigroup diffusion calculation to compute the inner iterations. The results of applying the program to the solution of several reactor configurations are compared with the results from a version of the PDQ code. For cell problems (with Neumann boundary condition), the new methods outperform the SOR method.