The work is devoted to balancing a two-stroke single-cylinder engine by installing one elastic hinge with a given characteristic between the strut and the crank. The hinge is an elastic element (spring or pneumatic spring) that moves between the guides of the calculated shape. To significantly reduce the lateral force acting on the piston, another elastic joint with preset force characteristics is located between the crank and the connecting rod. With certain parameters of the engine under consideration, in which an additional counterweight is located on the connecting rod at a certain distance from the connecting rod and crank connection point, the lateral force acting on the piston is zero at any time. When adding the characteristics of the elastic hinge located between the strut and the crank, with a known characteristic of the engine, such a total characteristic of the proposed system is obtained, at which the angular velocity of the crank will be constant. In this case, you can either completely abandon the flywheel in the engine design or significantly reduce its weight. At the moment, the considered problem has been solved for a certain constant crank speed. At a different speed, a different characteristic of the elastic hinge is required to ensure a constant crank speed. A possible solution to this problem can be the use of a pneumatic spring as an elastic element of the proposed hinges. The approach proposed here for balancing a two-stroke single-cylinder engine can be applied to balancing four-stroke engines.