A dispenser is disclosed for a solid or semi-solid product that includes an outer shell and a slider disposed inside the outer shell. The dispenser also includes an inner shell defining an opening and a carrier adapted to retain the product in the inner shell. The carrier includes carrier teeth that are engaged by an actuator connected between the slider and the carrier for advancing the carrier and the product. The actuator includes at least two drive arms that extend through the inner shell and into the carrier. The drive arms include drive teeth that are adapted to engage the carrier teeth. The carrier and product are replaceable, and the outer shell, the inner shell, and the actuator may be reused.