In this paper, we investigated the flow of an incompressible viscous fluid past a sphere which is oscillated one-dimensionally over flow regimes including laminar flow at Reynolds number of 100, 200 and Strouhal number of up to 5000. In order to analyze flow and estimate critical Strouhal number, we introduce three-dimensional vortex element method. With this method, separation only appears in decreasing velocity region during the high Strouhal numbers. We find out that vorticity distribution around sphere is proportionl to the Strouhal number. And we can decide that low Strouhal number is below 100, high Strouhal number is above 500 from many results. Thus the critical Strouhal number(St) effected to the flow field is expected to be 100<St<500.