To provide a support part structure for a lateral rod capable of further enhancing operation stability of a vehicle.

A lateral rod bracket 6 is downwardly extended from left/right one side part side of a vehicle body 3, and a lower end part of the lateral rod bracket 6 is connected to one end part of the lateral rod. A lateral rid brace 7 is laid between the lower end part of the lateral rod bracket 6 and a left/right central part of an underfloor member 5 positioned at a higher position than the lower end part of the lateral rod bracket 6 at a left/right central part side of the vehicle body 3, and a hook mounting member 10 is provided in the state that it extends in a vehicle longitudinal direction. An end part at the underfloor member 5 side of the lateral rod brace 7 is connected to the underfloor member 5 and the hook mounting member 10.