Dynamic stall phenomena have been investigated numerically by solving incompressible Navier-Stokes equations with a third-order upwind scheme in order to reveal the flow structure and mechanism of dynamic stall. The separated flows around a wing section at static attack angle are calculated and compared with the experiments which are conducted by the present authors. The results show excellent agreements with the experiments and the numerical scheme is proved to work well. Separated flows around oscillating airfoil in pitch are calculated by using the scheme and a moving mesh system. The flow conditions are selected from our experiments. The calculated separated region is small in pitching-up process and it becomes large in a pitching-down process. Quite different characteristics of flow patterns between in a pitching-up and pitching-down processes are obtained.