The possibility of using longitudinal critically refracted waves for acoustic strain gauging of longitudinal residual and temperature stresses in rails is studied. The influence of stress and temperature on the propagation velocity of elastic waves in rail steel is analyzed theoretically. An algorithm is presented for determining longitudinal stress in a rail by measuring the propagation time of longitudinal critically refracted waves. The operational principle is described, and the main parameters of an acoustic strain gauge device are presented, in which a differential scheme for measuring the propagation time of longitudinal critically refracted waves is implemented. Longitudinal critically refracted waves that propagate along a rail are emitted and received from the rolling surface of a rail head using contact piezoelectric transducers fixed on the polymethylmethacrylate wedges. The results of acoustomechanical and temperature tests are presented. The measurement errors are calculated. The results of determining the level of residual welding stresses in the head of a new rail are presented. The experimental results are compared with theoretical estimates of the stresses that arise in a rail under the influence of temperature, as well as with available data in the literature on residual stresses in rails.