Abstract: The load distribution among meshing screw threads is not uniform. The first meshing screw thread carries the biggest part of the load, as a result, the stress concentration is serious at the root of this thread. In this study, a new theoretical model, i.e., the combined beam–spring model, has been established by analyzing the stress and deformation of bolt connectors. Based on this model, the mathematical equations are derived, and the theoretical results of the load distribution of meshing screw threads and the stress concentration coefficients at the screw roots are obtained by calculation. Finally, theoretical results from the combined beam–spring model presented this paper and numerical results from finite element simulation of bolted connection are compared, which shows that two sets of results are consistent. The combined beam–spring model is proved to be applicable and effective in general engineering application, which can predict the nonlinear distribution among meshing screw threads and the stress concentration factors at the root of the threads.