We derive a delay-differential equation model that describes continuous-wave (cw) or passively Q-switched (PQS) two-frequency solid-state lasers submitted to frequency-shifted feedback (FSF). The study focuses on the locking of the beat note between the two free-running laser frequencies to a reference external frequency. The locking domain is obtained analytically in the cw regime. The PQS regime is treated by adding a saturable absorber population in the model equations. In this case, numerical simulations permit us to evaluate a locking range that is smaller than in the cw case. We find good agreement between the theoretical predictions and experiments carried out with a cw diode-pumped dual-polarization Nd:YAG laser as well as with previously published experimental results obtained with cw Er:Yb:glass [ Opt. Lett. 32, 1099 (2007)] and PQS Nd:YAG [ Opt. Lett. 33, 2524 (2008)] lasers. Applications of the FSF locking technique include the lidar-radar technique, for which a highly coherent beat note is required.