The present invention relates to a needleless injection device (1) comprising a reservoir (3), obturated by an upstream stopper (4) and a downstream stopper (5) between which a liquid active principle (6) is accommodated, and a receptacle (7) comprising at least one injection conduit (8), said receptacle comprising a cavity (10) whose height is equal to the distance travelled by the downstream stopper before each injection conduit is opened, - the height of the cavity in millimeters being between a minimum height and a maximum height, respectively defined by the following relationships, • minimum height = 3, • maximum height = 15 x exp. (-(V/9)2) +10, where V is the initial speed of ascent of the pressure profile expressed in bar per microsecond, - the ratio between the length of each injection conduit and the height of the cavity being between 1 and 2.
