This paper presents measurements of production cross sections and inelastic cross sections for the following reactions: 60 GeV/c protons with C, Be, Al targets and 120 GeV/c protons with C and Be targets. The analysis is performed using the NA61/SHINE spectrometer at the CERN Super Proton Synchrotron. First measurements are obtained using protons at 120 GeV/c, while the results for protons at 60 GeV/c are compared with previously published measurements. These interaction cross section measurements are critical inputs for neutrino flux prediction in current and future accelerator-based long-baseline neutrino experiments.