This study presents a novel, highly detailed, and accurate modelling method for calculation of the total annual solar thermal energy received by a double-slope solar still. The model is further utilized for sensitivity analysis and optimization with the help of Genetic Algorithm and TOPSIS methods. The model reveals that the main parameters that can independently affect solar energy input are the basin length, width, tilt angle, surface azimuth angle, and the glass covers’ inclination angle. The sensitivity of the annual solar energy input to all these parameters is analyzed. Moreover, all the parameters are chosen to be involved in the optimization problem. Sensitivity analysis results show that except for basin azimuth angle all other parameters significantly affect the amount of energy input to the solar still. Genetic Algorithm identified 60 optimum sets of parameters, one of which was selected by the TOPSIS method. The optimum values for the basin width, length, tilt and azimuth angles, and the inclination angles of the two glass covers are 2 m, 2 m, 8°, 180°, 80° and 67°, respectively. This design of a double-slope solar still will receive an annual total of 97.67 GJ solar energy input.