The four point explicit decoupled group (EDG) iterative method (A. R. Abdullah, 1991) and the explicit group (EG) method (D. J. Evans and M. J. Biggins, 1982; W. Yousif and D. J. Evans, 1986) were introduced as alternative numerical methods for the solution of elliptic p.d.e.'s. These methods were found to be suitable for parallel implementation (N. M. Ali and A. R. Abdullah, 1995; D. J. Evans and W. S. Yousif, 1990). In this paper, several parallel strategies for implementation on both EDG and EG methods for solving elliptic p.d.e.'s were introduced. The computational implementation of the strategies to both EDG and EG methods for solving elliptic p.d.e.'s on a MIMD Sequent Balance 8000 parallel computer are presented and discussed.