This paper presents measurements of the thickness-average residual stress imposed by laser peening near the edge of a thin sheet of a common titanium alloy. The slitting (or crack compliance) method was extended beyond its typical form to make residual stress measurements in this geometry. An analytical method was employed to optimize the experiment design for the near-edge, thin material geometry, where the design included the optimal number and position of strain gages and the most effective set of basis functions for stress computation. Two experiments were performed on a titanium strip that had been laser peened near the edge, using an optimal experiment design. Residual stress was found to be large and compressive near the edge of the sheet, with the compressive stress extending over 38% of the laser peened area.