Discrete-ordinates methods for the solution of the mono-energetic transport equation in infinite slab and infinite cylindrical geometry are considered. A numerical method for each geometry is defined, and successive over-relaxation schemes for accelerating the convergence of iterative solutions to each approximate equation system are illustrated. Numerical evidence is given to show that the successive overrelaxation schemes have a considerably higher rate of convergence than the standard Gauss-Jacobi iterative schemes. For the method for cylinders, the evidence shows also that the use of the acceleration technique results in a factor of at least 2.0 improvement in the actual time required to solve a range of problems to given accuracy.