This paper reports on a shell-model calculation of 59Ni and 59Cu. The nuclei are considered as threeparticle system outside a closed-core of 56Ni. The three particles are free to occupy the three orbits 2p3/2 1f5/2 and 2p3/3. For the two-body force, we have used the modified surface-delta interaction. Matrix elements of the Hamiltonian were computed and later diagonalized with the aid of a computer program. From these calculations, the binding energies of the three lowest states and those of the next higher states with the same spins and isospins were obtained. Also calculated, were the wave functions of these states.