This invention relates to a structure (1) for mounting an engine (2) under an aircraft wing (4), comprising a rigid structure (8) and means (10) of mounting this rigid structure under the wing, the mounting means (10) comprising a forward fastener (14) and an aft fastener (16). According to the invention, the forward fastener has at least one triangular shackle on each side of a vertical plane passing through a longitudinal axis (5) of the engine, placed in a vertical plane oriented along a direction inclined with respect to a longitudinal direction (X) and a transverse direction (Y) of the aircraft, and located in a horizontal plane defined by these directions (X) and (Y). Furthermore, the aft fastener comprises at least one shackle oriented along a vertical direction (Z) of the aircraft.