A subframe 1 is mounted on a vehicle body (body side frame 2) through mounts (subframe mounts B1-B6) with elastic bodies (rubber members 6, 7, 11), at two points located on both sides in lateral directions of a front portion of the subframe, at two points located on both sides in lateral directions of a middle portion thereof near a location where a suspension link is attached to the subframe 1, and at two points located on both sides in lateral directions of a rear portion thereof. The mounts at the points located on the both sides in lateral directions of the middle portion of the subframe each have a fracture stress upon crash smaller than that which the mounts at the points located on the both sides in lateral directions of at least one of the front and rear portions of the subframe 1 have. This subframe mount structure serves to mitigate damage of a passenger caused on collision of the vehicle to protect the passenger.