The loading capacity and ability of steel arch supports to accept deformations from the surrounding rock mass is influenced significantly by the function of the connections and in particular, the tightening of the bolts. This contribution deals with computer modelling of the yielding bolt connections for different torques to determine the load-bearing capacity of the connections. Another parameter that affects the loading capacity significantly is the value of the friction coefficient of the contacts between the elements of the joints. The authors investigated both the behaviour and conditions of the individual parts for three values of tightening moment and the relation between the value of screw tightening and load-bearing capacity of the connections for different friction coefficients. ANSYS software and the finite element method were used for the computer modelling. The solution is nonlinear because of the bi-linear material properties of steel and the large deformations. The geometry of the computer model was created from designs of all four parts of the structure. The calculation also defines the weakest part of the joint’s structure based on stress analysis. The load was divided into two loading steps: the pre-tensioning of connecting bolts and the deformation loading corresponding to 50-mm slip of one support. The full Newton-Raphson method was chosen for the solution. The calculations were carried out on a computer at the Supercomputing Centre VSB-Technical University of Ostrava.