A design procedure and numerical simulation of a production process for Cu-64 isotope by the 64Ni (p, n)64Cu nuclear reaction have been developed. The required radionuclide applicable in the nuclear medicine is produced through irradiating a cyclotron target of natural nickel with a proton beam. The process conditions were dictated by the capabilities of the cyclotron; an initial kinetic energy of 17 MeV (at a current of 10 µA) was fed into computation. As a result, dependencies of the Cu-64 isotope production on the target thickness and on the irradiation time were obtained. The target depth of proton penetration was investigated, and it was established where the peak radionuclide concentration was produced. An analysis of the obtained data made possible the finding of the optimal thickness of the nickel target being of 0.54 mm.