In this work is presented an analytical and numerical formulation for the analysis of thin and thick cylindrical shells, under internal and external pressure loads, utilizing the unidimensional Finite Element Method with variable number of nodes. In the numerical model, displacements associated to the nodal points are represented by displacement fields in the longitudinal and radial directions of the shell, verifying the restrictions of zero shear stress at the internal and external surfaces of the shell, in a combination of analytical solutions for thick cylindrical and spherical shells. Those displacement fields are represented by six degrees of freedom in each nodal point. The natural boundary condition of zero shear stress at the internal and external surfaces of the shell are guaranteed through the imposition of the linking between the model s degrees-of-freedom. The continuity between two adjacent elements and the fixation conditions of an element are imposed using the Penalty Method. The numerical results obtained from the implementation of the proposed model are compared with those provided by commercial software, for the work s validation.