This thesis addresses the problem of developing practical methods for estimating the execution time of SPMD, message passing, Fortran 77 programs. Performance estimating has been identified as a technology that is required to support the next generation of automatic parallelising compilers. Performance estimating tools could quantify the performance differences between functionally equivalent code sections in order to determine the optimum data layout strategies. This thesis assesses existing performance estimating methods and presents a new fast simulation technique. This fast simulation technique is applicable to a wider range of problems than previous methods and has made substantial improvements in accuracy by considering the effects of the memory hierarchy. An implementation of this method has been developed and is available with either a text-based interface or X-Windows/Motif GUI.