Based on two stress criterions（ the maximum circumferential stress criterion and average circumferential stress criterion） for U-notches under Mode-I,relationships among the critical notch stress intensity factor,the fracture toughness and the tensile strength were built separately,which follows the similar idea of Seweryn regarding the crack as a special U-notch with the notch radius equaling to zero. By means of the critical fracture loadings for U-notched plates under Mode-I and the finite element results of Ansys,a new method has been proposed to measure the fracture toughness and the tensile strength. The three point bending and tensile experiments in related references of PMMA and aluminum alloy specimens with single-edged U-notch and graphite tensile plates with central U-notch were verified. It indicates that the methods are simple and can be applied in engineering because the U notches can be machined conveniently and the fracture load under Mode-I can also be obtained easily.