One of the most difficult problems in building a distributed GIS lies in the heterogeneity of spatial databases. In particular, positional mismatches between spatial databases, which arise due to several reasons, may incur incorrect query results. They result in unreliable outputs of query processing. One simple solution is to correct positional data in spatial databases at each site, according to the most accurate one. This solution is however not practical in cases where the autonomy of each database should be respected. In this paper, we propose a spatial query processing method without correcting positional data in each spatial database. Instead of correcting positional data, we dynamically transform a given query region or position onto each space where spatial objects of each site are located. Our proposed method is based on an elastic transformation method by using delaunay triangulation. Accuracy of this method is proved mathematically, and is confirmed by an experiment. Moreover, we implemented using common use database system for usefulness verification of this method.