A vibrating machine including a first machine part that vibrates in operation, a second machine part connected to an installation area of the vibrating machine, and a vibratory drive. A resilient bearing is arranged between the machine parts and has at least one air spring per support point and at least one compressed air reservoir fluidically connected to the air spring. A throttle is switched intermediate the air spring and the compressed air reservoir. The first machine part bearing has a resonant or natural frequency lower than an operating frequency of the vibrating machine. The bearing system has a frequency-dependent lower stiffness level with high damping at low frequencies, an upper stiffness level with low damping at higher frequencies, and a transition zone at an intermediate transitional frequency. The throttle is dimensioned such that the transitional frequency is close to, preferably slightly above, the resonant or natural frequency.