A subframe structure being supported by a vehicle-body frame and supporting a vehicular power plant through a damping device. The subframe structure includes: a longitudinal member which extends in a front-rear direction of a vehicle and is rigidly fixed to the vehicle-body frame; a lateral member which extends in a vehicle width direction and on which at least one of the damping devices is mounted; a floating mechanism which floatingly supports the lateral member on the longitudinal member through an elastic mechanism; and a suspension arm connected to the longitudinal member.