Several vector and parallel processing algorithms for the inherently recursive Sn method are developed for two-dimensional curvilinear geometries. The iterative sweeps through the spatial and directional meshes are decomposed into various independent subdomains suitable for multiprocessing on shared memory architectures. Both spatial decomposition (using both axial and radial groups) and angular decomposition (using directional groups) are used. The new algorithms are implemented on the six-processor Cornell National Supercomputing Facility IBM 3090/600J computer using the IBM parallel Fortran compiler. The algorithm behaviors are investigated using a series of r-z cylindrical geometry fixed-source problems. In addition, to verify the algorithm performance for realistic problems, a two-group, r-θ geometry, pressurized water reactor (PWR) source calculation is performed. Total speedups as high as 5.86 are observed for the PWR model compared with the one-processor solution. The suitability of these algorithms for highly parallel architectures is also discussed.