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Simulation of the aircraft assembly process is an important problem arising from the airline industry. To address this problem, a methodology was developed in previous studies, which is based on the contact problem solving. This paper is devoted to further development of numerical methods for simulation of fuselage junction riveting process. The methodology of a contact problem solving was developed to simulate the aircraft assembly process. In the developed algorithm, the initial contact problem is transformed into the problem of quadratic programming with linear constraints. As the installed fasteners restrict relative tangential displacements of assembled parts in the junction area, the relative tangential displacements are negligible in comparison with normal ones. This special feature of the problem justifies implementation of node-to-node contact model that is much simpler than general surface-to-surface model.However, this implementation imposes the restriction that all finite element nodes of parts in the contact area should coincide completely. This restriction creates difficulties during mesh building because it is much easier to build meshes of the parts independently from each other. The main contribution of this paper is introducing the method and extending the existing algorithm for airframe assembly simulation to the case of non-conformal meshes. This article introduces the method and the modernized algorithm for the riveting process with non-conformal meshes. [ABSTRACT FROM AUTHOR]