The logging evaluation of shale fracability is significant for the selection of high-quality reservoir targets and the construction of staged fracturing. The factors affecting shale fracability are complex, and the analysis and weight selection of the factors in traditional logging evaluation methods are obscure, thus resulting in low evaluation accuracy. In this paper, the shale oil reservoirs in the Liushagang Formation in the Weixinan Depression are divided into three types: the matrix type, texture type, and interlayer type. Then, a 3D digital core model is established to characterize the reservoirs in the Weixinan Depression. Through finite-element simulation, sensitivity analysis, and an analytic hierarchy process, the sensitivity and relative weights of the factors affecting the fracability of different types of shale oil reservoirs are determined. Finally, the evaluation model of fracability for different types of shale oil reservoirs is established, and the reliability of the model is verified by the comparison with fracturing data. The main factors affecting the fracability of target layers include mineral composition, textures, and fractures. The minerals with the most significant influence on elastic parameters are quartz and clay. Texture density has the most significant influence on the texture-type shale oil reservoir, and fractures mainly affect the interlayer-type shale oil reservoir. The fracability evaluation model established in this paper allowed the classification and accurate evaluation of reservoir fracability through the microscopic analysis of rocks and the quantification of influencing factors, which largely determined the accurate and efficient development of shale oil and gas.