Flow through compliant tubes with linear taper in wall thickness is numerically simulated by finite element analysis. For verification of the numerical method, flow through a compliant stenotic vessel is simulated and the results are compared to the existing experimental data. Steady two-dimensional flow in a collapsible channel with initial tension is also simulated and the results are compared with numerical solutions from the literature. Computational results show that as cross-sectional area decreases with the reduction in downstream pressure, flow rate increases and reaches the maximum when the speed index (mean velocity divided by wave speed) is near the unity at the point of minimum cross-section area, indicating the flow limitation or choking (flow speed equals wave speed) in one-dimensional studies. for further reductions in downstream pressure, flow rate decreases. The flow limitation or choking consist of the main reasons of waterfall effect which occurs in the airways, capillaries of lung, and other veins. Cross-sectional narrowing is significant but localized. When the ratio of downstream-to-upstream wall thickness is 2, the area throat is located near the downstream end. As this ratio is increased to 3, the constriction moves to the upstream end of the tube.