A multi-link engine is provided with an upper link, a lower link and a control link. The upper link is pivotally connected to a piston by a piston pin. The lower link is rotatably mounted on a crankpin of a crankshaft and connected to the upper link by an upper pin. The control link is rotatably connected to the lower link by a control pin and pivotally mounted on a pivot portion of a control shaft. The links are configured and arranged with respect to each other such that inertia forces of a prescribed second or higher order in terms of an engine rotational speed act on at least the upper link and the control link in a transverse direction of the engine with a sum of leftward and rightward inertia forces of the prescribed second or higher order being substantially zero.