Among various types of shells, shells of revolution have extensive use in various industries. For example in structures such as liquid reservoirs, silos, cooling towers and tunnels which in many cases are reinforced by stringer stiffeners. Due to these shells are subjected to various dynamic loadings during their exploitations, cognition of their dynamic characteristics such as natural frequencies, has been considered by researchers. The aim of this dissertation is development of an appropriate finite strip in curvilinear coordinate of the axisymmetric shell and in direction of its meridian, for free vibration analysis of this type of shell, according to Reier-Mindlin shell theory. The effect of meridian stiffeners is considered by calculating its stiffness and mass matrix in place of middle surface of the shell. In longitudinal direction of the strip, Lagrange polynomials are used as the shape functions, which easily make it possible to consider various type of middle and edge point supports. In the examples which have been investigated, it was illustrated that by using a few nodes in longitudinal direction of strip, we would get good results, which this reduces the number of total degrees of freedom of the problem, and time and cost of calculation. In the various chapters of this thesis, accuracy and efficiency of proposed method to determine the natural frequency of shells of revolution with different geometry and Gaussian curvature, are studied. In addition, convergence of results and variation of some parameters such as thickness, boundary conditions, geometry and number of stiffeners are investigated.