An apparatus for dispensing a fluid comprises a housing and a resilient liner adapted to hold the fluid disposed in the housing. A fluid transfer mechanism is in fluid communication between the liner and an applicator assembly mounted on the housing for dispensing the fluid on the skin of the user. The applicator assembly includes an actuator movable relative to the housing so as to activate the fluid transfer mechanism when the actuator is reciprocated. A fluid delivery element is held in contact against skin of a user for applying the fluid onto the skin. The fluid delivery element is supported on the actuator to be movable together with the actuator by varying contact pressure with the skin. Each movement of the actuator generates continuous negative pressure within the liner for drawing fluid through the fluid transfer mechanism and collapsing the liner.