The application of superconducting Bi2Sr2CaCu2O8 and YBa2Cu3O7 wires or tapes to electronic devices requires the optimization of the transport properties in Ohmic contacts between the superconductor and the normal metal in the circuit. This paper presents results of tunneling theory in superconductor-normal-metal-superconductor (SNS) junctions, in both pure and dirty limits. We derive expressions for the critical-current density as a function of the normal-metal resistivity in the dirty limit or of the ratio of Fermi velocities and effective masses in the clean limit. In the latter case the critical current increases when the ratio γ of the Fermi velocity in the superconductor to that of the weak link becomes much less than 1 and it also has a local maximum if γ is close to 1. This local maximum is more pronounced if the ratio of effective masses is large. For temperatures well below the critical temperature of the superconductors the model with abrupt pair potential on the SN interfaces is considered and its applicability near the critical temperature is examined.