A fluid dispenser device having a fluid reservoir (10), a pump (20) mounted on the reservoir (10) for selectively dispensing the fluid, and a dispenser head (30) connected to the pump and incorporating a dispenser orifice (31). The device includes at least two laterally-actuated elements (40, 50) distributed around the dispenser head (30), the laterally-actuated elements (40, 50) being displaced simultaneously in a direction that is approximately transverse to the central axis of the device, and each co-operating with a peripheral edge (11) of the reservoir (10) so as to exert an axial force thereon.