PURPOSE: To suppress transfer of vibration and noise of an engine to a vehicle body by means of a restricting member in an engine supporting device provided with the restricting member for restricting a displacement of the engine toward the right and left directions of a vehicle.

CONSTITUTION: Liquid chambers 17a and 17b and connecting lines passing through the liquid chambers 17a and 17b are formed in either of main body rubbers 16 of a lateral rod 10 which restricts the displacement of an engine toward the right and left directions of a vehicle. An electric heological fluid 30 is filled in the chambers and lines. In a control device 20, an ECU23 inputs signals from sensors 21 and 22 and calculates an acceleration applied to the engine ins the right and left directions. When the acceleration in the right and left directions exceeds a specified limit, voltage is applied to the fluid 30 to increase the viscosity of the fluid 30 and to increase the rigidity of the lateral rod 10. When it is below a specified limit, the voltage is not applied to it to remain the viscosity of the fluid 30 at a low level. Thus the rigidity of the lateral rod 10 can be reduced enough to prevent the transfer of vibration.