To provide a fitting structure of a compact oil cooler whereon planar and semicircular elements are arranged in parallel, which promotes heat exchange by uniformly conducting oil in respective semicircular parts and provides a required capacity by using plural modular oil coolers.

Peripheral edges of a pair of plates 2, 3 formed in a planar and semicircular dish shape are fluid-tightly joined with each other and inner fins 6 are formed therein, and oil entrances 1 are arranged on both end parts. The inner fins 6 are an offset type where many rising faces 7 with a planar and circular shape are concentrically formed and a pitch P1 in the radius direction of the rising faces 7 is formed to be larger as to outside in the radius direction.