We present a mathematical model of flows driven by pumping without valves(valveless pumping). We consider the two dimensional elastic tube immersed in an incompressible fluid. In this paper, we observ the pressure difference and the net flow when the width of the tube changes. We tilt the width of the tube symmetrically, so that the widths of both ends are different. We enforce periodic and symmetric force to the elastic tube and observe the direction of the net flow. Under various circumstances, we numerically study the effect of valveless pumping.