Abstract: The classic approximate formula proposed by Creager and Paris is generally used to calculate the opening stress of three-point bending U-notched beams along the bisector, but the scope of application is very limited. The modified formula proposed in this paper widens its application scope and can be applied to almost the whole tensile region of the ligament along the U-notch bisector. Integrating the opening stress along the U-notch bisector over the fracture process zone length and dividing the integral by the length, the average opening stress is obtained. Once it reaches the critical value, the average stress failure criterion with two material parameters, namely tensile strength and fracture toughness, is derived. Based on this criterion, a new method of concurrently measuring the two material parameters of quasi-brittle materials using three-point bending U-notched beams is proposed. A series of experiments are carried out for U-notched beams with same notch depth but different root radii, and critical loads in three-point bending are obtained. With the derived stress concentration factors, the average stress failure criterion is used to generate a series of over-determined equations, where the tensile strength and fracture toughness as two unknowns can be solved readily with a proper numerical method.