Modelling slab track-bridge interaction subject to a moving train usually involves solving complex high-dimensional matrix equations which is time-consuming. This research works to optimize the auto-assembling process in the slab track-bridge coupling matrices formulation and improve the computational efficiency by truncating the dynamic matrices used in time integral scheme. To achieve the above goals, the key issue is to appropriately couple the systems’ dynamic matrices in conditions where the elemental sizes of the track slab and the bridge are inconsistent in 3-D space. Besides, by firstly clarifying the degrees of freedom vector of the rail, the track slab and the bridge girder participated in each time step, dynamic matrices characterizing the train-slab track-bridge interaction are truncated with time to reduce the matrix size. This present study has demonstrated the solutions for above problems. Apart from model validations, some numerical examples are presented to show applicability of the proposed methods.