In connection with efforts to utilize the CRAY-1 computer efficiently, we present some methods of analysis of rates of convergence for block iterative methods applied to the model problem. One of the more interesting methods involves relaxing on p x p blocks of points. A Cholesky decomposition is used for that smaller problem. One of the basic methods of analysis is a modification of a method discussed earlier by Parter. This analysis easily extends to more general second order elliptic problems.