A case (1) for a stick of material to be applied by friction, in particular a stick of lipstick, including: a hollow cylindrical inner body (2), having a main axis (X), open at a proximal end (5), capable of receiving the stick of material; a hollow cylindrical outer body (7), having a main axis (X), open at a proximal end (10), into which the inner body (2) is inserted such as to pivot relative to the outer body (7) about the main axis (X), an outer cylindrical surface (4) of the inner body (2) facing a cylindrical inner surface (8) of the outer body (7); the case also including one flexible lip (34) for controlling the rotation torque about the main axis (X) of the inner body (2) inside the outer body (7).