A method for repairing in vivo torn cartilaginous or other bodily tissue, particularly torn meniscus tissue during arthroscopic surgery, employs a repair tack of biodegradable material chosen to have a degradation time in excess of the required healing time for the tissue. The repair tack has a shaft portion with a longitudinal bore and a grip portion adapted for releasable engagement by a hollow applicator. In one embodiment the grip portion of the tack is a cross bar, at the proximal end of the shaft, which fits into an open-sided slot at the forward end of the applicator. A needle passes through the hollow applicator and tack bore to project from the distal end of the tack shaft. With the tack supported in the slot and the needle passing through the stem, the needle and tack can be inserted into the joint cavity through a portal in the skin or through an insertion cannula. The sharpened needle point is placed in contact with the torn tissue and force is applied to the holder and the needle to cause the needle and the tack to penetrate the tissue to a desired depth. The point of the needle is then withdrawn into the axial opening of the applicator and the cross bar is displaced from the slot, thereby leaving the tack firmly secured in the tissue.