Structural dynamic analysis of an arbitrary structure such as vehicle structure can be carried out using finite element method or other numerically oriented approaches. Analytical approach is usually preferred due to its convenience for parametric studies, however such an approach can usually be followed for limited class of geometries only.In the present work, a method which was proposed by Barboni, Gaudenzi, Mannini and Santini, which modified the well known transfer matrix method by expanding the governing differential equations for the structural state vector into a power series, with the power related to the eigenvalues of the dynamic eigenvalue problem, is followed and rederived. The procedure is first applied to basic bending and torsional oscillation of beams, and the results are compared to analytical solution. Next the problem of structure with arbitrary geometry is analysed. For this purpose, the bending oscillation of non-prismatic beam is considered. Previous formulation can readily be applied for piecewise continuous approximation to the structure.