Within an effective Lagrangian approach and resonance model, we study the and reactions via the -exchange mechanism. For the reaction, we perform a calculation of the differential and total cross-sections by considering the contributions of the intermediate resonance decaying into and then into . Besides, the non-resonance process is also considered. With a lower mass of , the experimental data for the invariant mass distributions can be fairly well reproduced. For the reaction, with the model parameters, the total cross-section is of the order of 10 μb at the photon beam energy ~2.5 GeV. It is expected that the model calculations in this work could be tested by future experiments.