This open access book delves into the realms of geotechnical engineering and solid mechanics. In order to establish fracture parameters that are both relevant and conducive to safety, the book extensively investigates the fracture mechanical properties of mode I, mode II, and mode III in brittle rock materials. Various fracture testing methods and fracture mechanics theories are employed for a comprehensive examination. To provide a theoretical interpretation of the fracture test results, the book presents detailed derivations of established fracture criteria. Additionally, new fracture criteria are introduced to enhance fracture prediction models. Targeted at graduate students, scientists, and engineers engaged in the study of rock fracture mechanics, hydraulic fracturing, and material mechanics, this book serves as a valuable resource.