A hydraulic power transmission unit includes a casing connected to an engine, a pump member fixed to the interior of the casing and a turbine mounted within the casing and connected to an output shaft, whereby the output torque of the engine is transmitted to the output shaft through fluid in the casing. A damper mechanism includes damper springs mounted directly on the inner face of the casing at its outer circumference. A damper disc serves to transmit the power of the engine to the output shaft through the damper springs. A lock-up clutch mechanism is also housed within the casing and includes a frictional engagement element arranged between the damper disc and the output shaft. The lock-up clutch mechanism is operated, i.e. frictional engagement element selectively applied and released, by a clutch piston slidably mounted within a cylinder defined by the damper disc.