Reliable software testing is a time consuming operation. In addition to the time spent by the tester in identifying, locating, and correcting bugs, a significant time is spent in the execution of the program under test and its instrumented or fault induced variants. When using mutation based testing to achieve high reliability, the number of such variants can be large. Providing a software testing tool that can efficiently exploit the architecture of a parallel machine implies providing more computing power to the software tester and hence an opportunity to improve the reliability of the product being developed. In this thesis, we consider the problem of utilizing high performance computers to improve the quality of software. We describe three approaches to the parallelization of mutant execution on three architectures: MIMD, Vector, and MIMD with vector processors. We describe the architecture of the P\sp{\rm M}othra system designed to provide the tester a transparent interface to parallel machines. A prototype, constructed by interfacing the Mothra system to an Ncube through a scheduler, was used to conduct the experiments reported in this dissertation. Analysis of algorithms developed and experimental results obtained on these three architecture are presented. Our results enable us to conclude that the MIMD machine, as typified by the Ncube, is superior to some other architectures for mutation based software testing