A method for varying the spring rigidity of an elastomer engine mount, such as for motor vehicles, includes bringing one of two at least intermittently simultaneously loadable parallel-connected spring bodies into continuous engagement with supports and bringing the other of the two spring bodies into intermittent contact with supports as a function of predetermined operating parameters, for absorbing induced forces in parallel with the two spring bodies. The other spring is connected in parallel with a force brought to bear separately from the outside for causing it to contact its supports. An elastic engine mount for motor vehicles includes a hollow-cylindrical spring body and a solid-cylindrical spring body disposed concentrically relative to one another between an engine mount plate and a support plate to be fixed to a vehicle body. According to one embodiment, a diaphragm is disposed between the lower end surface of the solid-cylindrical spring body and the support plate for defining a hollow chamber between the diaphragm and the support plate. The hollow chamber operatively connects the solid-cylindrical spring body with the plates upon forced introduction of hydraulic fluid into the hollow chamber. According to another embodiment, a mechanical plunger is disposed between the lower end surface of the solid-cylindrical spring body and the support plate. A threaded bolt engages the mechanical plunger. A control motor drives the threaded bolt and operatively connects the solid-cylindrical spring body with the plates.