This paper describes fundamental studies on free stream acceleration effect on drag force in bluff bodies. The flow with gradual velocity increase assumed an accelerated flow. The wind tunnel tests were conducted in order to investigate the difference of aerodynamic characteristics between non-accelerated flow and accelerated flow. The experimental models were a circular cylinder and a square cylinder. In an accelerated flow, the condition of free stream was an acceleration of about $3.6m/s^2$. Experimental Reynolds number varied between form $4.0{ imes}10^4$ to $1.64{ imes}10^5$. The pressure distributions and the aerodynamic force were measured in both case of non-accelerated flow and accelerated flow. In case of a circular cylinder, the drag of accelerated flow is lower than that of non-accelerated flow in the low Reynolds number regime. Then, it becomes higher than that of non-accelerated flow in the high Reynolds number regime. On the other hand, in case of a square cylinder, the drag of accelerated flow is higher than that of non-accelerated flow in the whole Reynolds number regime. If a separation point can be movable such as the circular cylinder, the additional momentum due to flow acceleration leads to delay separation and to decrease the drag in the low Reynolds number regime. If a separation point is nearly fixed such as a square cylinder, the additional momentum due to acceleration always affects to increase the drag than that of non-accelerated flow. Based on this research, it is expected that the roof shape of high speed train where the separation point is movable has the advantages to reduce the effect of accelerated flow such as strong crosswind/gust.