Cu/NbTi multilayer thin films and superconducting wires were fabricated and heat treated with conventional annealing and analyzed by differential scanning calorimetry (DSC) as a basic study for the enhancement of Jc. Interfacial reactions of Cu/NbTi multilayer thin films and superconducting wires were investigated with optical microscope, SEM, and XRD. According to the effective heat of formation (EHF) model, CU$\_$3/Ti was predicted as a first phase. However, considering the crystalline structure and thermodynamics, CuTi was predicted as a first phase. According to the results of DSC and XRD, CU$\_$2/Ti was found to be the first phase, followed by the formation Of CU$\_$4/Ti. The difference in first crystalline phase between the experimental result and the predicted one was discussed. In case of Cu/NbTi superconducting wires, the compounds formed at the Cu/NbTi interface grew with annealing time and the amount of compounds formed in Nb-47wt%Ti alloy was larger than that in Nb-50wt%Ti alloy. It seemed that the incubation time for the formation of compounds in Nb-50wt%Ti alloy was longer than that formed in Nb-47wt%Ti alloy. Also, the diffusion was the rate controlling step for the growth of compounds in all specimens. These compounds were formed at 500-600.deg. C for I hour annealing and, thus, the drawing time below I hour must be required to minimize the growth of compounds for the enhancement of Jc.