Abstract: Based on the general governing equations of elastic thin shells, 1-order ordinary differential matrix equation for the state vector of revolutionary shells is firstly derived. This equation is essential for using transfer-matrix method to analyze general revolutionary shells. By means of the extended homogeneous capacity high precision integration method, static and dynamic solutions are obtained conveniently. Several examples demonstrate the validity and high efficiency of the proposed method. This approach extends the research of the transfer-matrix method, and lays the foundation of the semi-analytical research of structural vibration and acoustics for revolution shells with variable thickness.