An engine support structure improves energy absorbing efficiency at the vehicle body frame in relation to impact input from the vehicle front to rear direction. The support structure includes a vehicle body frame having front frame side members extending in the front to rear direction of the vehicle, a sub-frame disposed below the vehicle body frame and that supports the engine, and connecting members that connect the front frame side members and sub-frame. A suspension device for an automobile prevents insecure tightening. A support member which connects a body vehicle side member and sub-frame is provided with an outer tubular member connected to the sub-frame and that extends in the upper to lower direction, an inner tubular member mated into the upper portion of outer tubular member, and an insulator mated into inner tubular member and whose length in the upper to lower direction is shorter than outer tubular member.