Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded connection is difficult to measure. So it is necessary to study the reliable numerical method. At present neither the convergence analysis of the computational results nor the elastic-plastic analysis in the loading-unloading process are studied. In this paper, von Mises plasticity and kinematic hardening model is used to describe the material response. A new convergence criterion for nonlinear finite element analysis of the loading-unloading process is proposed. An axisymmetric finite element model according to the proposed convergence criterion is developed and used to analyze the distributions of axial-load and stress. It can be conclude that the stress distribution analysis is more dependent on the mesh density than the axial-load distribution analysis. The stress distribution result indicates that with increasing of applied load, the engaged threads close to the nut-bearing surface become plastic firstly. The axial-load distribution result reveals that the load percentage carried by single thread depends on the position of thread and load intensity. When the load is relatively small, the applied load is mainly carried by the engaged threads near the nut-bearing surface, when the load is larger, the differences of percentages for all threads become small. The proposed convergence analyzing procedure is applicable for other nonlinear analyses. The obtained distributions of axial-load and stress can be a reference of engineering application.