Dynamic loss of stability of a rod under longitudinal load lower than the Eulerian load was studied. The finite velocity of propagation of longitudinal waves in the rod is taken into account. These waves provide the conditions for occurrence of the parametrical resonance, which can be implemented also at loads lower than the Eulerian one. The possibility of occurrence of instability is established at a suddenly applied axial load, which is lower than the Euler load. This instability can appear only at the rod length falling in one of the intervals. If the load is applied continuously, the amplitude increase rate of transverse oscillations decreases together with the increasing forward-front length. Low forces of viscous resistance cannot interfere with a significant increase in amplitude. The introduction of nonlinear terms into consideration in the absence of resistance transfers the system into the beat mode with the subsequent pumping of the energy of longitudinal oscillations to the transverse ones and vice versa.