Energies for 524 levels of Ar XIII, 460 levels of Ar XIV and 156 levels of Ar X V have been calculated using the GRAS code of Dyall et al. (1989, Comput. Phys. Commun, 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 1%, whereas results for other parameters are probably accurate to better than 20%. Additionally, the level lifetimes derived from our radiative rates are in excellent agreement with measured values.