Numerical simulation for the axisymmetric body with contractive and dilative periodic motion is carried out. The present analysis shows that a propulsive force can be obtained in highly viscous fluid by the contractive and dilative motion of axisymmetric body. An axisymmetric code is developed with unstructured grid system for the simulation of complicated motion and geometry. It is validated by comparing with the results of Stokes approximation with the problem of uniform flow past a sphere in low Reynolds number($R_n$ = 1). The validated code is applied to the simulation of contractive and dilative periodic motion of body whose results are quantitatively compared with the two dimensional case. The simulation is extended to the analysis of waving surface with projecting part for finding out the difference of hydrodynamics performance according to variation of waving surface configuration. The present study will be the basic research for the development of the propulsor of an axisymmetric micro-hydro-machine.