A spool of traverse wound double-sided PSA tape and method of making same. The PSA tape includes an adhesive body with an upper adhesive surface releasably adhered to a bottom side of a release liner having a release value. At least one reinforcing strand is disposed longitudinally through the adhesive body. The PSA tape is traverse wound onto a core in successive winding layers with each successive winding layer producing an outer winding layer with the bottom side of its adhesive body crossing at an angle over the top side of the release liner of a preceding inner winding layer. The tensile strength of the at least one reinforcing strand is greater than a Resistance Bond of the outer winding layer to the preceding inner winding layer.