With the growth and advance of the petroleum industry there is a need for better transportation facilities for liquid and gaseous materials. Concerns are raised with respect to savings in materials in structures and environmental problemas connected with failures and spills. Usual transportation media are cilindrical tubes, functioning as pipelines embedded in the soil or supported by it. It is quite important to know better the structural properties of cilinders, such as its stability when subjected to compressive forces and moments. The advances in computational analysis allow us to develop new sophisticated mathematical models for finite element analysis.The objective of this work is to provide an analytical model for structural analysis of pipelines, based on beam finite elements (including axial and bending deformation), enhanced with cylindrical shell deformation modes. The resulting finite element has a hierarchical formulation with combination of convencional polinomial modes and trigonometric functions. The effect of a Winkler- type elastic foundation is also included.Basic examples of static and buckling analysis of tubes in elastic media are studied, using a program for numerical and symbolic computation (Mathcad), varying the tube geometry and the foundation constants. The results obtained are critical loads and respective buckling modes, which are compared to the available theoretical results.