Abstract: There are three phases in the solutions to the differential equation of Timoshenko beam on Pasternak foundation. Based on the displacement solutions to the differential equation of all phases, the displacement, rotation, shear force and moment at any cross-section can be expressed by the nodal displacements and rotations. When the shear forces and moments at nodes are evaluated, a transcendental finite element is formulated, in which the homogeneous solutions of displacement and rotation are used as the displacement model in essence. The essential boundary condition of the variational principle requires that the total shear should be implemented as the nodal shear. The theoretical formulae to calculate the distribution of shear force between the Pasternak foundation and Timoshenko beam is derived based on the finite element formulation. A conventional finite element formulation based on the displacement interpolation functions of the Timoshenko beam element is established. The transcendental finite element owns excellent convergence property, whose calculation accuracy does not depend on the mesh density. The results of examples demonstrate that the results of transcendental finite element and conventional finite element are consistent with the theoretical solutions. Even there is only one element meshed, it still achieves the exact results. There are some theoretical inaccuracies in the finite element formulation existed in other literatures, which lead to remarkable errors. For elastic beam on hard foundation (the phase is Δ>0), the actions of load only affect the local place subjected to the load directly, for other places, the actions of load can be neglected.