The transfer matrix of the distributed mass shaft model for the helicopter oblique drive tail shaft is derived. The bending moment, lateral displacement, shear distortion, moment of inertia, gyroscopic moment and axial force are all considered in the model. The transfer matrix of the diaphragm coupling and elastic support are established. The calculation method of the critical speed of the tail drive shaft is presented. In order to test the validity and precision of the presented method, the results of horizontal shaft with three supports are compared with those of the finite element method. The maximum error of the presented method with respect to the finite element method is 4.1%, which indicates that the presented method is high in calculation accuracy and quick in calculation speed. Consequently the presented method is very suitable for the designers to analysis the influence factors of critical speeds of tail drive shaft system.