The most expensive spatial operation in patial database in a spatial join which computes a combined table of which tuple consists of two tuples of the two tables satisgying a spatial predicate. Although the execution time of sequential processing of a spatial join has been so far considerably improved the response time is not tolerable because of not meeting the requiremetns of interactive users. It is usually appropriate to use parallel processing to improve the performance of spatial join processing. in spatial database the fixed grids which consist of the regularly partitioned cells can be employed the previous works on the spatial joins have not studied the parallel processing of spatial joins using fixed grids. This paper has presented an analytical cost model that estimates the comparative performance of a parallel spatial join algorithm based on the fixed grids in terms of the number of MBR comparisons. disk accesses, and message passing, Several experiments on the synthetic and real datasets show that the proposed analytical model is very accurate. This most model is also expected to used for implementing a very important DBMS component, Called the query processing optimizer.