Abstract A new technique is presented for solving the linear equations arising in reservoir simulation using multiple processors in parallel. The Nested Factorization(1) algorithm is extented by domain decomposition in a highly parallel way while ensuring that the power of the method is retained as the computation is distributed over several processors. The method is illustrated by the fully implicit solution of a three phase simulation of a 4800 cell problem on a 6 processor Silicon Graphics machine giving an overall speed up factor of about 2.8.