To rationalize the setting of joint parameters, model size, and initial value of vertical stress in simulation of mining of steeply inclined coal seams, a fault tree analysis method of discrete element numerical simulation was used and a mathematical model was proposed. A method of eliminating the influences of size-effect errors on the parameters of coal and rock samples was obtained based on previous work. Furthermore, the constitutive equation and eigenvalue determination formula of a joint discontinuity surface were established, and a method of determination of the joint parameters was proposed, forming the complete “coupling chain” between parameters for numerical simulation. In addition, a formula for the initial value of vertical stress was constructed by way of the compression and shear model of the element body. Also, the minimum dimension was determined by means of strength factor analysis of fracture mechanics. Taking the research literature as an example, the model size and initial value of vertical stress were calculated. On this basis, the physical parameters of coal samples, the physical parameters of coal rocks considering the influence of the size effect and the calculated coal rock joint parameters considering the influence of size effect were directly used to comparatively analyze the displacement and stress fields, thus verifying the reasonability and correctness of the mathematical model.