A damper includes: an inner cylinder defining an inner chamber, having a slidable contact piston; an outer cylinder outside the inner cylinder and defining a reservoir chamber between the inner outer cylinders; and a damping-force control device controlling damping force by controlling a flow rate of an operating oil between the inner reservoir chambers. The control device includes a valve seat externally, projecting from the outer cylinder, having an opening for a first communicating channel connected to the inner chamber and an opening for a second communicating channel connected to the reservoir chamber, a valve element opening and closing on the valve seat by electromagnetic force, and a cap defining a variable pressure chamber between the cap and the valve element, and integrally holds the valve element and the valve seat. The variable pressure chamber can be connected to the first and the second communicating channels.