The most costly spatial operation in spatial databases is a spatial join, which combines objects from two data sets based on spatial predicates such as, intersects or contains. Even if the execution time of sequential spatial join processing has considerably been improved over the last few years, the response time is far from meeting the requirements of interactive users.In this paper, we have designed 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. Three kinds of methods of task allocation for improving their performances: static, dynamic, semi-dynamic have been examined for determining which task allocation strategy based on grid files shows the best performance. The experimental tests have been conducted on the MIMD parallel machine; with shared disks conclude that the first join algorithm based on disjoint decomposition of data space outperforms the second based on non-disjoint decomposition. Also, the semi-dynamic task allocation method is the best.