Attempts to perform synthesis of a passive vibroinsulation two-mass system intended for the simultaneous reduction of machine frame vibrations and forces transmitted to foundations by supporting elements were undertaken in the study. In view of the variable frequency of the machine operation, it was necessary for the frequency interval, encompassed by the vibroinsulation system operation, to be within given limits. On the grounds of properties of the linear massive-elastic system formulated in the works of Genkin and Ryaboy (1998), the problem of vibroinsulation system synthesis was formulated in the parametric type optimisation approach with equality and inequality limitations. For piston compressor vibroinsulation, the mass and elasticity matrices of the vibroinsulating system, as well as its physical structure, were determined. Its operation was verified on the basis of simulation investigations, taking into account the system loss and transient states.