The long-term goal of the project is to create and justify a reliable mathematical model that expresses the efficiency of geometrical shapes of non-tracking flexible solar panels. However, the amount of solar energy absorbed by a non-tracking flexible solar panel depends on many parameters: the direction of the sun beam, reflected light, and temperature, etc., which would make a complete model mathematically complicated. In the current model, we limit our consideration to the direction of the sunbeam. In order to simulate the exposure of the panel, we describe the trajectory of the Sun and base the model on the mathematical flux that uses the sun rays as the vector field. To be precise, the efficiency of a geometrical panel is defined as the flux density, which is the ratio of the mathematical flux and the surface area. Our current model was evaluated for the latitude of New York City and we determined the efficiency of the optimized at panels, cylindrical panels, and conical panels. The analysis was largely done through geometrical studies and numerical integration with software programs Python, Maple, Mathematica, and MATLAB.