PURPOSE: To make the transmission of engine vibration and difficult restrain the occurrence of bubbles by mounting the upper and lower ends of an oil cooler between a down tube of a frame suspended from a head pipe to the front side of the engine and the front end of an oil tank mounted on the lower side of the engine.

CONSTITUTION: While an engine 1 mounted on the lower front part of a frame 2 of a motor cycle has the front upper end of an engine case 3 fastened to left and right stays 6 at the lower end of a downing tube 5 directed from a head pipe of the frame downward, the engine 1 is supported by fastening the rear lower end to the lower end of a frame center 7. An oil tank 8 is disposed at the underside of the engine case 3, the front upper part of the oil tank 8 is fastened to the front lower part of the engine case 3 and the rear end is fastened to the lower end of the frame center 7. An oil cooler 9 is disposed on the front side of the engine case 3 to floatingly support the upper and lower parts by a cushion cylinder 11 or the like so as to make the vibration of the engine 1 difficult to be transmitted.