Understanding the behaviour of DNA is important to gain insight in biological processes, including translation, transcription, gene repair and so on. However, DNA also has interesting mechanical properties that can, for instance, be used in designing novel materials. Single-molecule studies show that double-stranded DNA, when subjected to tension, undergoes a sharp transition from its native, helical ground-state to an overstretched, unwound state that is 70\% longer. Intercalating molecules, for example used for visualisation purposes, greatly affect this transition. The equilibrium properties of both the overstretching and the effect of intercalators can be modelled using a multi-state Kuhn model. Upon using intercalators with slow kinetics, relative to the stretching velocity, different behaviour is observed, which is not captured by the equilibrium model. To understand this out-of-equilibrium behaviour of intercalator-DNA complexes under tension, a different approach is needed. In this thesis, we develop a simulation method that combines molecular dynamics with kinetic Monte Carlo to study the effect of intercalator binding dynamics on the mechanical properties of DNA. We find that our simulations both reproduce experimentally observed force-extension curves and show qualitatively identical kymographs. Furthermore, at constant intercalator concentrations, we observe universal behaviour for identical ratios of the stretching velocity and intercalation rate.