A belt strap windup device for eliminating a belt slack of a safety belt system of a motor vehicle upon the motor vehicle exceeding a predetermined vehicle deceleration. The windup device includes a belt roll-up mechanism, a shaft which is constantly acted upon by a retractor, and a windup reel to which the belt is mounted. A pulley is coupled with the shaft at least upon the predetermined deceleration of the vehicle, and an electrically ignitible propellant charge is arranged centrally with respect to the shaft, with the charge being adapted to act upon a driving fluid after an ignition thereof so as to operate the pulley so as to eliminate the slack in the belt. A belt strap mounting recess is provided in an interior of the shaft with a longitudinally aligned belt passage slot and with an insert opening lying at the end face of the shaft. The shaft includes a number of annularly arranged axially aligned ducts filled with the driving fluid, with the ducts terminating at an end face of the shaft. The fluid in the ducts is adapted to be acted upon by the propellant charge after an ignition thereof.