The dual band microstrip antenna is realized by placing open circuit stub on the edges of the patch. When the stub length is taken to be nearly quarter wave in length, it offers capacitive and inductive impedance around the resonance frequency of the patch and realizes dual frequency response. In this paper, a detail analysis for the effect of stub on the dual band response of rectangular microstrip antenna is presented. The surface current distributions and the resonance curve plots were studied. It was observed that the stub modifies the fundamental and higher order orthogonal mode resonance frequencies of the patch and realizes dual frequency response. With an increase in stub length the directions of surface currents are modified, which gives broadside radiation pattern at the dual frequencies. The formulation of resonant length at dual frequencies in terms of stub dimensions is proposed and they agree within 5% with that of the simulated results.