Accurate determination of breakdown pressure in the presence of pre-existing fracture (e.g., natural fractures or perforations) can assist engineers better manage expected fracture gradients. The classical models by Hubbert and Willis, and Haimson and Fairhurst did not account for the existence of pre-existing fractures in predicting breakdown pressure. In addition, the available fracture models for the calculation of breakdown pressure do not consider nonlinear internal pressure distribution in the pre-existing fracture. Finally, some of them either ignored near wellbore stress concentrations, or they are limited to specific fracture dimensions. To overcome the limitations of current methodologies, a weight function method is applied to predict breakdown pressure of two general symmetrical radial fractures emanating from a borehole. A weight function parameter table and three weight function parameter correlations are provided for continuous dimensionless crack lengths from 0.001 to 100. For uniform pressure distribution in the pre-existing fracture, the weight function based breakdown pressure is compared against the PSA method [Paris and Sih, 1965; Abou-Sayed et al., 1978], the results show a good agreement. Weight functions are applied to predict breakdown pressure for uniform and nonuniform pressure distribution in a pre-existing fracture, and the results prove that the pressure distribution affects the breakdown pressure. Sensitivity studies are conducted to investigate the influence of pre-existing crack length, orientation, in-situ stress contrast, and fracture toughness on breakdown pressure. It indicates that breakdown pressure (1) does not always increase with increasing dimensionless crack length at different stress contrast, and (2) increase with increasing absolute value of deviation angle and fracture toughness. The weight function based breakdown pressure is further verified against measured breakdown pressure from laboratory hydraulic fracturing experiments by finetuning fracture toughness. The results are also in good agreement for selected successful fracturing experiments.