The most costly spatial operation in spatial databases is a spatial join with combines objects from two data sets based on spatial predicates. Even if the execution time of sequential processing of a spatial join has been considerably improved over the last few years, the response time is far from meeting the requirements of interactive users. In this paper, we have developed two kinds of parallel spatial join algorithms based on grid files: a parallel spatial join using a multi-assignment grid file and a parallel spatial join using a single-assignment grid file. We also present the cost of the two join algorithms in terms of the number of MBR comparisons. The experimental tests on the MIMD parallel machine with shared disks show that the first join algorithm based on disjoint decomposition of a data space outperforms the second based on non-disjoint decomposition.