A transmission device includes a casing elongated towards a power transfer aperture, a power output member rotatably supported in the aperture by a first bearing, and a power transfer shaft with an outer end rotationally coupled to the power output member and an inner part supported from the casing by a second bearing. The shaft has an axial aperture for receiving lubricating oil and a radial aperture communicating thereto for squirting out lubricating oil radially as the shaft revolves. An oil shield cover has a base mounted to the casing, an extension elongated under the shaft from the base towards the first bearing, an end wall reaching upwards from the end of the extension towards the shaft with the lowest point of its upper edge closely approached thereto at an axial position on the shaft at which its diameter is substantially less than where it is supported by the second bearing. The extension rises on either side of the shaft at least to the height of the lowest point of the upper edge of the end wall, and has an opening on its upper part corresponding to the radial aperture. A space for pooling lubricating oil ejected from the radial aperture is defined by the oil shield cover and the casing, and as lubricating oil accumulates therein it first can escape by overflowing over the end wall of the oil shield cover. The lubricating oil pool at this stage reaches high enough to wet the lower portion of the first bearing.