A procedure is presented which allows the application of linear response theory and the random phase approximation to an open shell. The procedure is applied to Ca isotopes. The general features of giant multipole resonances are found to vary smoothly with the mass. The resonances exhibit more structure in the open 1f 7 2 shell nuclei. While the energy-weighted dipole sum is practically constant in all isotopes, the isoscalar quadrupole and octupole energy weighted sums increase continuously by ~ 30 % from 40Ca to 48Ca.