The interaction of the lateral surface of an axially cylindrical prism with the fluid flow is studied. The prism moves in a translational motion (without rotation) in a fixed fluid, such as air. The effectiveness of such a reduced interaction analysis is important in reducing vehicle drag as well as increasing the speed of technical sports vehicles. Accordingly, the task of increasing the interaction forces involves extracting energy from the fluid. In the mathematical problem, the force of resistance of the prism to fluid movement, its minimum or maximum value, is chosen as the optimization criterion. The interaction between the prism and the fluid is described in an unconventional way, without using the concepts of drag and lift forces, but using the relationships of classical mechanics. For this purpose, the interaction of the prism with the fluid is divided into two zones: the pressure zone (in front of the prism) and the suction zone (at the back of the prism). Interactions with changes in the amount of motion of a fluid in a differential form are obtained. The relationships found are integrated in the simplest cases: for example, when the surfaces of a prism are broken planes. Two dominant forms of the prism are considered: the surfaces are only convex or the surfaces are only concave. Parametric optimization problems are solved numerically with a computer. As a result, optimal shapes are obtained for the minimum criterion and the maximum criterion. The main result of the research is the application of a new theory of fluid mechanics, which allows analytical or numerical solving of analysis, optimization and synthesis problems with the obtained formulas, without the use of space time programming, which would need to change the object shape, flow rate and direction in almost every integration step.