A numerical and analytical analysis of shear-induced melting in smectic-A liquid crystals is presented. Based on a Landau expansion of the complex smectic order parameter, equations governing the phase and amplitude of the local density modulation are found. Numerically solving these equations indicates that for a range of parameter values a first-order transition, from a shear-stressed to a more relaxed state, is periodically encountered as the total shear is increased. Suitable approximations allow the analytic determination of certain characteristics of this first-order transition.