Rock is one of the main construction materials for engineering structures. Its tensile strength (ft) and fracture toughness (KIC) are the key characteristics significantly influencing the safety of engineering structures, and determining these parameters is critical for designing underground engineering structures, such as mining, tunnels, and water conservancy. Therefore, this study focuses on developing a theoretical model based on the cracked straight through Brazilian disc (CSTBD) test, which allows for the simultaneous determination of ft and KIC for rocks. The proposed model provides a comprehensive understanding of the material properties by deriving expressions for the nominal stress (σn) and equivalent crack length (ae) using the CSTBD approach. Further, the research employed the normal distribution method to assess the variability of individualized fracture toughness and tensile strength parameters. By applying this model, statistical values of fracture toughness and tensile strength can be obtained, facilitating comparative analysis of test results for different rock types and validating the efficacy of the proposed model. Furthermore, the relationship between material parameters (ft &KIC) and peak load (Pmax) was established through CSTBD, enabling reliable prediction of experimental peak load with 95% reliability.