In the design of ship propulsion system, the study of oscillation is a great importance because they play a decisive role in the operating ability of the shaft system. Among ship shaft oscillations, axial oscillation has been only a particular interest after applying on ships for diesel engines with ratio of piston stroke and its diameter 3-4,4. In this paper, the special features of the computational model are presented when studying the axial oscillations on the ship shaft system. It should be emphasized that the system of differential equations in describing the free and forced oscillations can be obtained directly from the analogous equations of the torsion oscillation. However, unlike the torsional oscillation, the axial oscillation of the ship shaft system directly affects the hull through the thrust bearing. In order to solve with the problem of determining the forced and resonant axial oscillations based on the Runge-Kutta numerical method is done by directly integrating the system of 2nd order differential equations in describing the oscillations. Therefore, the paper presents the research results in proposing a procedure to reduce the order of 2nd order differential equations and providing an algorithm to solve the system of differential equations in describing axial oscillations. From that, it will be considered that the mechanism under which forces of variable value are applied to it, axial oscillation occurs. The accuracy in calculating of the axial oscillation depends not only on the accepted method of determining the free and forced oscillation, but also the proper in giving the parameters of the discrete model. If the masses are easy to calculate, the evaluation of the axial deformation of the crankshaft is not univariate because there are many formulas given on the basis of idealizing the crankshaft under the structure of bar. Hence, it is proposed to build a 3D model and determine the deformation of the engine crankshaft components by the finite element method.