A torque transmitting device for transmitting torque by utilizing the viscosity of a fluid includes a casing having a cylindrical barrel having closed opposite ends, shafts rotatably supported in the casing in concentric relation to the cylindrical barrel, a fluid chamber defined by an inner peripheral surface and outer peripheral surfaces of the shafts, a plurality of annular outer plates disposed in the fluid chamber and rotatable with the casing, a plurality of annular inner plates disposed in the fluid chamber alternately with the outer plates and rotatable with the shafts, and a fluid filled in the fluid chamber. Torque can be transmitted between the casing and the shafts through the viscosity of the fluid present between the outer plates and the inner plates. Flow passages are defined in the fluid chamber and extending axially of the shafts for allowing the fluid to flow in the fluid chamber axially of the shafts.