This book presents the formulation for predicting exact eigenvalues of shells of revolution by using the Wittrick-Williams algorithm and dynamic stiffness method. Free vibration partial differential equations (PDE) of shells of revolution are degraded analytically into series of ordinary differential equations (ODE). The set of ordinary differential equations is rewritten in the Hamilton form, from which dynamic stiffnesses are computed using the ODE solver COLSYS. A solution for solving the number of clamped-end frequencies J0 in the Wittrick-Williams algorithm is also provided for both uniform and non- uniform shell segments. Based on the theories, a Fortran code has been developed and is available. The book aims