The problem of dynamic stability of a simply supported rod subjected to axial jump loading is considered. A systematic application of the method of expansion in terms of the normal axial and bending vibration modes is utilised. Longitudinal vibrations give rise to periodic longitudinal forces which in turn causes unstable bending vibrations. Application of the Galerkin approach results in a system of ordinary differential equations with periodic coefficients which are reduced to Mathieu equation. The instability regions whose form depends on the spectral properties of the longitudinal and flexural vibrations, damping values and longitudinal force are obtained. An example of unusual shapes of the instability regions is shown: the twelfth transverse mode caused by the first longitudinal mode turns out to be unstable for some parameters of the rod. The critical value of the jump load leading to instability of the considered transverse vibration modes is derived.