A wound closure tape applicator has an elongated trapeziform casing partitioned into a front supply chamber for a roll of adhesive tape carried on a backing strip or liner and a trapeziform rear storage chamber for collecting waste backing strip. Front and bottom walls of the casing form a tape outlet slot in a lower front corner of the supply chamber. A cylindrical post extending horizontally between the casing sidewalls internally adjacent the slot guides the tape downwardly along the front wall. A front end portion of the bottom wall projects upwardly close to the underside of the post and guides the liner rearwardly to peel it away from the tape as the latter is pulled downwardly through the opening. A false bottom wall in the casing guides the liner rearwardly along the bottom wall beneath the partition into the rear chamber. The front wall includes a brake flap which is resiliently deflectable to press the tape against the post to separate an applied segment of the tape from the roll along the perforations and to control tension in the tape being applied. The tape but not the liner is perforated and notched at regular intervals along its length. The tape is preset or "aged" in roll form so that when the waste liner is fed into the storage chamber it will coil without regard to the shape of the chamber.