Electronic devices installed inside moving objects may experience significant impulse and vibrational mechanical loads, causing combined translational and rotational vibrations in these devices. In this paper, we investigate the possibility for realizing passive vibration isolation of a vibration-protected block from angular vibrations provoked by the translational movements of the supporting structure. Mathematical modeling of the block reaction to external force factors has been carried out within the framework of the classical theory of rigid body dynamics. The mechanical characteristics of the dampers included in the device were evaluated in the physical experiment. Parametric analysis of numerical solutions showed that the amplitudes of angular vibrations of the protected block depend on the position of its center of rigidity relative to the center of mass, as well as on the spatial orientation of the dampers and their elastic and dissipative characteristics. The set of parameters was determined, which guarantees that the arising angular vibrations of the protected unit will not exceed the admissible values.