An attachment device for an aircraft engine that includes a rigid structure and an attachment mechanism of the engine to the rigid structure. The attachment mechanism includes a device reacting to thrust forces generated by the engine, the reacting device including two link rods mechanically connected to a balance beam at a rear end by a first mechanical connection, a main fitting fixed to the rigid structure to which the balance beam is mechanically connected, and two additional fittings fixed to the rigid structure to which the link rods are mechanically connected with play. The mechanical connections between the balance beam and the main fitting and between the link rods and the additional fittings each include a pin orthogonal to a mid-plane of transmission of the forces.