In this paper, we present the elastic bunch graph matching as a new approach for iris recognition. The task is difficult because of iris variation in terms of position, size, and partial occlusion. We have used the circular Hough transform to determine the iris boundaries. Individual segmented irises are represented as labeled graphs. We have combined a representative set of individual model graphs into a stack like structure called an iris bunch graph (IBG). Finally, a bunch graph similarity function is proposed to compare a test graph with the IBG. Recognition results are given for galleries of irises from CASIA version and UBIRIS databases. The numerical results show that, the elastic bunch graph matching is an effective technique for iris matching. We also compare our results with previous results and find that, the elastic bunch graph matching is an effective matching performance.