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Transients from lightning strikes can enter underground cables at overhead line to power cable transitions. Possible overvoltages on these surges at cross-bonding connections of the cable screens are of major concern. A model is developed for modelling overvoltages from transient signal propagation through a combined cross-bonding cable and box. This model is applied to the first Dutch 400 kV cable connection. Such model incorporates model parameters whose values depend on design details of the cross-bonding box. The values for these model parameters are extracted from the measured transmission and reflection signal on steep pulses injected into the actual cross-bonding box configuration. The model combines transmission line description for the cross-bonding cables with mainly inductive behaviour of the cross-bonding box. The obtained results are verified by measurements. The model is applied to investigate overvoltages induced at the cross-bonding cable and box on 1.2/50 µs impulse voltage injection representing a lightning impulse voltage applied to the core conductor of the cross-bonding cable. Furthermore, the effectiveness of surge arresters to reduce overvoltages at the cross-bonding cable screen is demonstrated by simulations with this model in PSCAD.