Method for mounting an aircraft pylon connected to a wing by at least one front wing attachment comprising: - at least one first plate secured to the wing which has a first contact surface, - at least one second plate secured to the pylon which has a second contact surface, - a plurality of final connection elements which, when the pylon is mounted, connect the first and second plates (38, 40) by holding the first and second contact surfaces against one another at a plane of contact that is inclined for each final connection element, the first and second plates (38, 40) respectively comprising a pair of first and second through-holes (52, 54), - at least one shear pin which, when the pylon is mounted, straddles a pair of first and second receptacles (60, 62) which are respectively provided in the first and second plates (38, 40) and which each have a cross section identical to that of the shear pin, such that the mounting method comprises: - a step of pre-positioning the first and second contact surfaces (S38, S40), such that the first and second contact surfaces (S38, S40) are approximately parallel and close to or in contact with one another, and of approximately pre-aligning the first and second through-holes (52, 54) of each pair of first and second through-holes (52, 54) and pre-aligning the first and second receptacles (60, 62) of each pair of first and second receptacles (60, 62), - a step of installing and tightening temporary connection elements in certain pairs of first and second through-holes (52, 54), so as to keep the first and second contact surfaces (S38, S40) clamped against one another, - a step of installing and expanding at least one radially expandable element in at least one pair of first and second receptacles (60, 62), - a step of installing and tightening final connection elements in at least some of the pairs of first and second through-holes (52, 54) that are not occupied by the temporary connection elements, - steps of removing the radially expandable element(s) and installing the shear pin(s), and of removing the temporary connection elements and installing the final connection elements. - at least one first plate secured to the wing which has a first contact surface, - at least one second plate secured to the pylon which has a second contact surface, - a plurality of final connection elements which, when the pylon is mounted, connect the first and second plates (38, 40) by holding the first and second contact surfaces against one another at a plane of contact that is inclined for each final connection element, the first and second plates (38, 40) respectively comprising a pair of first and second through-holes (52, 54), - at least one shear pin which, when the pylon is mounted, straddles a pair of first and second receptacles (60, 62) which are respectively provided in the first and second plates (38, 40) and which each have a cross section identical to that of the shear pin, - a step of pre-positioning the first and second contact surfaces (S38, S40), such that the first and second contact surfaces (S38, S40) are approximately parallel and close to or in contact with one another, and of approximately pre-aligning the first and second through-holes (52, 54) of each pair of first and second through-holes (52, 54) and pre-aligning the first and second receptacles (60, 62) of each pair of first and second receptacles (60, 62), - a step of installing and tightening temporary connection elements in certain pairs of first and second through-holes (52, 54), so as to keep the first and second contact surfaces (S38, S40) clamped against one another, - a step of installing and expanding at least one radially expandable element in at least one pair of first and second receptacles (60, 62), - a step of installing and tightening final connection elements in at least some of the pairs of first and second through-holes (52, 54) that are not occupied by the temporary connection elements, - steps of removing the radially expandable element(s) and installing the shear pin(s), and of removing the temporary connection elements and installing the final connection elements.