The invention relates to a device for injecting a filling material in the fluid phase into a canal space, the said device comprising an adaptor, an automatic mixer connected to the said adaptor, an intra-oral injection tip fitted at the upper end of the said automatic mixer, and is characterized in that the said injection tip is a tube the distal end of which has an outside diameter smaller than or equal to 1.5 mm over a length greater than or equal to 8 mm, in that the said injection tip is made of a shape memory material so that it can be bent to a desired orientation, in that the said injection tip is moulded at the upper end of the said automatic mixer, and in that the said injection tip comprises, on its exterior surface: *either circular ribs defining a groove, the upper end of the automatic mixer being moulded into this groove so that the said injection tip is locked in position in the said upper end while at the same time retaining a degree of freedom to rotate about its axis of symmetry, *or one or more mutually parallel circular ribs, the upper end of the automatic mixer being moulded onto this circular rib in such a way that the said injection tip is blocked in position in the said upper end while at the same time retaining a degree of freedom to rotate about its axis of symmetry.