The paper presents an analysis of linear models track response under longitudinal loads due to braking/accelerating of the train. Longitudinal forces are uniformly distributed on the whole length of the train. Analysis was carried out under assumption that – in the short time – train speed not changes significantly. Therefore stationary response of rail track is considered. The problem of critical speed has been analyzed. Effect of damping properties of track foundation on maximum longitudinal displacements were also considered. In summary certain practical conclusions were formulated as well as the further investigations were pointed out.