We propose a method of estimation of glue bonded joint of metal casing and circular composite shaft. A distribution of tangential stresses in the glue layer when a torque and an axial force are applied is determined. It is shown that the level of tangential stresses produced by the torque is by an order of magnitude greater then that produced by the axial force. In order to reduce the maximum tangential stresses, it is proposed to cut the metal casing aslant from the edge to the center, and a corresponding method of estimation of glue bonded joint is developed. It is proven that under the total length of the slant equal to 0.5 m, when the metal casing length is equal to 3 m, the peak of the stresses is halved. The methods of estimation developed are applied to analysis of a real joint of metal casing and composite shaft.