This article discusses the use of Petri nets to model the process of object matching between an image and a model under different two-dimensional geometric transformations. This transformation finds its applications in sensor-based robot control, flexible manufacturing systems, industrial inspection, and so on. Its topological structure relation, called point-line relation structure (PLRS), presents a Petri net-based description approach for object structure. It has been shown how Petri nets can be used to model the matching process, and an optimal or near optimal matching can be obtained by tracking the reachability graph of the net. The experiment result shows that objects can be successfully identified and located under two-dimensional transformation such as translations, rotations, scale changes, and distortions due to partial object occlusion.