Provided is an engagement position storage device capable of detecting a clutch engagement position of a vehicle finely and a brake system including such a device. In an engagement position storage device 2b that stores an engagement position of a clutch to engage and disengage power of a vehicle, when the vehicle becomes a traveling state in predetermined duration after acceleration in a front-back direction of the vehicle changes, the engagement position storage device 2b stores a clutch engagement position based on a clutch position detected when the acceleration changes. A brake system 1 includes a wheel latching mechanism 5 that latches wheels of a vehicle by driving a propelling member 5a by driving devices 3 and 4; and a controller 2 that controls driving of the propelling member 5a of the wheel latching mechanism 5 based on a clutch engagement position stored in the engagement position storage device 2b.