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In this paper the influence of the two-parameter elastic soil on the dynamic behavior of a beam with variable cross-section is examined, in the presence of conservative axial loads. The beams are assumed to follow the well-known Timoshenko hypotheses, in order to take into account both the rotary inertia and shear deformation effect. The Rayleigh-Ritz approach is used and Boundary Characteristic Orthogonal Polynomials are chosen as trial functions; (BCOPs method [2]). The theory is concisely presented in a matrix form, so that the contribution of the rotary inertia and of the soil can be easily recognized. Various examples and comparisons are illustrated, in order to emphasize the influence of the soil properties and of the beam taper ratio. Finally, the results are also compared with the results given by other authors, using exact and approximate approaches. [ABSTRACT FROM AUTHOR]