Laser processing of thin flexible ceramics and glasses is challenging due to the incurred brittleness and unfavorable thermal and optical properties of such materials. We describe an alternative laser cutting method which utilizes surface stress raisers to cleave brittle substrates along a defined path. An ultrashort laser source is used to precisely pattern a plurality of aligned elliptical recesses on the material surface. The apex of an ellipse concentrates applied tensile stresses. Depending on the elliptical dimensions, the achievable stress concentration factor can be up to 50. The orientation of the ellipses defines a preferred scribing path. The technique was successfully applied to thin flexible yttria stabilized zirconia ceramic and borosilicate glass substrates. The form and properties of the material play an important role during the fracture process. Polycrystalline ceramics were found to accurately auto cleave along the path due to stresses produced during the laser ablation. The resulting fractured surface is of higher quality and strength than surfaces cut using full body laser cutting techniques, while the crystalline phase is preserved. The optical setup is simple, low cost, and compatible with roll-to-roll manufacturing.