Theoretical analysis of vibrations of a system in which the mass is connected with the support in series of more than one elastic element had shown that there is possibility to provoke additional resonances. Condition of it is change of damping values of the system near the supposed resonance frequency defined calculations. Feed mechanism of cylindrical grinding machine of older design was researched from that point of view. The mechanism consists of chain of elastic elements in series connecting the wheelhead with the bed of machine. Large friction forces exist in the chains of elements and in the wheelhead ways. Analysis results are presented in the paper.