This paper presents the optimal shape of a compound trapezoidal cross-section by considering sensitivity analysis of design variable in shape optimization of trapezoidal open channel. the sensitivity analysis of the effect of discharge and channel bottom slope on design variables, constraints and objective function. The objective function is to minimize the cost of excavation and lining and the cost of water lost as seepage and evaporation losses, the design variables are the depth and width of the channel bottom, side slopes and free board, the constraints include uniform flow, maximum and minimum velocity, Froud number and water surface width. Optimization was performed with different values ​​of discharge and channel bottom slope in two stages and with several models. In the first stage, at a constant slope, with increasing discharge, the values ​​of discharge, bed width, free board, flow velocity, flow cross-sectional area and cost increase, but the side slope decreases. in the second stage, at constant discharge values, as the slope of the channel bottom increases, the values ​​of flow depth, bed width, flow cross-section area, and overall channel construction cost decrease. Results of sensitivity analysis show that all of design variables are important .