Three external tooth wet friction materials are each composed of an external tooth plate and a lining adhered to one surface thereof along an entire circumference. Three internal tooth wet friction materials are each composed of an internal tooth plate and a lining adhered to one surface thereof along an entire circumference. Then, the three external tooth wet friction materials and the three internal tooth wet friction materials are disposed side by side so as to constitute a multi-plate frictional engagement apparatus. A thickness of the internal tooth plate is made thinner in view of its good heat discharge capability, and the thickness of the external tooth plate is made thicker by that much.