Accurate prediction of loads on mechanical couplings is crucial in assessment of loads on coupled structures, and in reliable prediction of the motions of coupled bodies. This thesis presents a numerical articulation method, which is capable of modeling various mechanical couplings. The proposed numerical method relies on contact elements.</br> The first objective of the work is to prove the eligibility of contact elements in representation of mechanical couplings, and to highlight the shortcomings and positive aspects of contact elements for this representation. The second objective of the thesis is to study the influence of different hydrodynamic, kinematic, and coupling models on the motion behavior of articulated bodies and coupling forces. To accomplish these objectives extensive and systematic studies on a twofold pushing convoy are conducted.</br> The convoy bodies are interconnected with hinge joints. The hinges are modeled by means of kinematic constraints, and with contact elements. Frequency and time domain boundary element methods with linearized motions of equation, as well as a Reynolds-averaged Navier-Stokes (RANS) code coupled with a nonlinear kinematic solver are used to compute the body motion responses and coupling forces. The simulation results are compared to model basin measurements. It is shown that the contact element model can simulate mechanical couplings efficiently and it provides a suitable method to idealize free and suppressed modes at articulation locations. Furthermore, it is shown, that RANS in association with the nonlinear equation of motion and kinematically constrained joints, as well as boundary element methods in adherence to the contact element model provide more accurate prediction of articulation forces, and motion responses of coupled bodies.</br> However, frequency and time domain boundary element methods with kinematically constrained joints still deliver agreeable and reliable results. Moreover, a case study is presented, in which a river-sea pushing convoy is applied in time domain numerical simulations. The convoy bodies are interconnected with prismatic joints and are free to heave and pitch relative to each other. Prismatic joints are modeled by means of contact elements.</br> The case study demonstrates a successful application of contact elements in simulation of complexly articulated multibody systems. Furthermore, the findings obtained in this work contribute sustainably to the numerical approaches in assessment of hydrodynamic and articulation loads on mechanically coupled floating bodies.