While several models have been developed to predict the failure pressure of pipelines with corrosion defects, relatively few models are available for pipelines with cracking defects. The goal of this study is to develop an unbiased and accurate probabilistic burst failure pressure model for thin-walled pipelines containing a single, longitudinally-oriented, crack-like defect. A comprehensive database is first established, consisting of experimental and numerical data collected from literature as well as numerical data obtained from the extended finite element method (XFEM) conducted in this study. The failure pressure prediction model is developed by adding a correction factor to the modified Ln-Secant method, a semi-empirical model previously developed. The correction factor is modeled using a multivariate linear regression that considers the pipe properties and defect characteristics as independent variables. The proposed model delivers unbiased and less variable failure pressure predictions. A case study of an example pipeline with a crack like defect shows that the failure pressure model plays a critical role in the risk management of pipelines through a life-cycle cost analysis.