A drive shaft assembly particulary suited for power transmission in motor vehicles wherein a drive shaft has a universal joint connected to at least one end thereof with a sealing boot attached in sealing engagement between the outer joint member of the universal joint and the drive shaft. The invention is particularly directed to the provision of an elastomeric cover on the outer surface of the drive shaft, the elastomeric cover extending along the shaft from the exterior of the sealing boot to within the region enclosed by the boot in order to provide an arrangement which is resistant to damage, corrosion, and wear and which may be conveniently fitted and assembled. The elastomeric cover may be provided with internal ribs to establish ventilation channels for the shaft assembly.