Cracks due to manufacturing processes or in-service applications can propagate and cause failure in structures. Therefore, it is of interest to find a suitable fracture assessment method for predicting crack initiation. Main approaches for fracture assessment of structures are global approach and local approach. In the global approach, it is assumed resistance against fracture can be measured by a critical values of a far from crack tip parameter like K or J. In this study, Beremin model of local approach is used for predicting brittle fracture which studies stress and strain fields at the crack tip. The model introduces unknown parameters which have to be calibrated using experimental fracture data. The purpose of this study is evaluating of conventional calibration methods of local approach parameters using the experimental brittle fracture data of three point bending specimens, determining limitations, and finally presenting a new calibration method to produce suitable parameters for predicting brittle fracture of the specimens by using local approach to fracture. This study shows that conventional calibration method using experimental fracture data of three point bending specimens has limitation in some cases. Also, by introducing location parameter of Weibull distribution as a stress triaxiality criteria in Beremin model, a new rational method for predicting brittle fracture of the three point bending specimens with different constraints is presented.