In this study, an investigation is carried out to analyse earthquake induced pounding between two insufficiently separated base isolated buildings in considering the behaviour of elastically or inelastically the response of structures. In this study, both buildings are modelled as six-storey and four-storey systems to simulate the structural behaviour. Moreover, non-linear viscoelastic impact elements are applied to model collisions at different storey levels using three ground motion records with different peak ground accelerations. Two different cases are carried out in this study: (1) two adjacent buildings connected with non-linear viscoelastic dashpot dampers are considered to be elastic and (2) both adjacent buildings are considered to be inelastic. A formulation of the equation of motion for two different cases is presented in this study. The effect of the insufficient gap distance on the response of structures is also investigated. The results of the study prove that pounding of buildings to behave inelastically has considerable influence in order to obtain the accurate behaviour of the structures under earthquake excitation.