Coupling loss properties were studied theoretically and experimentally for three superconducting conductors of the Rutherford cable type which were developed for a 1kWh/1MW-SMES. The strand of the conductor has a CuNi/Cu mixed matrix and a Cu core; its surface is not insulated. The experimental results showed that the inter-strand coupling loss of the conductor is much smaller than the intra-strand coupling loss when the compression stress corresponding to the designed value of the electromagnetic force for the SMES was applied to the sample conductor. We also measured the crossover resistance between strands of the conductor by means of the four probe method, and estimated the contact surface resistance by taking account of the result of an analog simulation with an electric circuit model. By using the contact surface resistance obtained, we could theoretically explain the experimental result of the loss. As for the intra-strand coupling loss, the effect of the existence of a Cu core and a CuNi cladding around it on the loss was also discussed.