In this work, an enriched finite element model is developed for structural simulation on vessels of pressure subjected to axial rotation and under internal and external pressure loads. An analytical solution for displacement, in some cases, is recovered without applying interpolating functions, as usually done on commercial finite element software. So, interpolating functions for displacement comes from combining previously known analytical solutions such: the solution for cylinders under zero axial strain, for cylinders under rotation and for the sphere. Each element was formulated using for four nodes, arranged axially on middle surface of the cylindrical shell. To each nodal point it is associated seven degrees-of-freedom, referring to the coeficients of the displacement function, on axial and radial directions. The development of an enriched finite elements has the advantage of choosing a function that best quantify the nodal point results, with no need of a high number of elements to obtain numerical convergence of the method. In addition, to ensure displacement continuity between two adjacent elements, certifying that beyond the same displacement the first derivative is continuous, the penalty method is applied. Finally, the variation of stress through the thickness of the vessel of pressure is considered, on the numerical model.