Building pounding is a recognised phenomenon where adjacent buildings collide under lateral loading due to insufficient provision of building separation. The consequences of this interaction are known to be complex, and both buildings’ responses can be significantly affected. In the absence of extensive experimental data, numerical modelling has been frequently adopted as a means of evaluating building pounding risk during earthquakes. In performing numerical analysis, it becomes necessary to create specialised ‘contact’ elements to simulate building contact. While many contact elements have been previously proposed, detailed consideration of their inherent assumptions has frequently been overlooked. This thesis considers the significance and consequences of using the Kelvin contact element for a variety of pounding situations and with varying levels of model detail. Pounding between two adjacent floors (floor/floor collision) is considered as a one dimensional wave propagation problem. By modelling each floor as a flexible rod (termed distributed mass modelling), theoretical relationships for collision force, collision duration and post-collision velocity are derived. This theory is then compared to the predictions made when using the traditionally adopted assumptions of fully rigid colliding floors (termed lumped mass modelling). The post-collision velocities obtained from each method are found to agree only when the axial period of both floors is identical. Relationships between lumped mass and distributed mass models are formed, and an ‘equivalent lumped mass’ method is developed where distributed mass effects can be emulated without explicit modelling of floor flexibility. The theoretical solution method is then adapted for use in Non-Linear Time History Analysis (NLTHA) software to model specific pounding situations. Numerical modelling of a single collision is performed to compare these results to the theoretical predictions. Good agreement is found, and the model’s complexity is simplified until a sufficiently accurate simulation is performed without overly onerous computational requirements. Five methods are detailed that incorporate energy loss during collision into the distributed mass models and a calibration method is developed that enables researchers to define the level of energy loss that occurs during a single collision. Using the developed modelling methods, the pounding response of two existing Wellington buildings is predicted. This is first performed using 2D analysis of the stiffest frame from each building. The predicted building pounding damage is categorised into local damage (damageresulting from the magnitude of the force applied during contact) and global damage (damage due to the change in dynamic building properties resulting from momentum transfer during collision). Local and global damage effects are found to be fundamentally different consequences of collision, with the two categories responding differently to changes in the modelled system. The effects of building separation, scaling of input motion, modelling of soil-structure-interaction, collision damping, and floor rigidity are investigated for the considered system. 3D analysis of the building configuration is then investigated. Additional complications arising from the transverse movement of buildings prior to and during collision are identified and refined modelling methods are developed. The 3D configuration of these buildings causes torsional interaction, despite both buildings being perfectly symmetrical. This torsion is due to the eccentric positioning of the buildings relative to each other, which causes an eccentric contact load when pounding occurs. The 3D models are used to test the effects of building separation, 2D vs. 3D modelling, collision damping, floor rigidity, and the significance of the torsional interactions. Attention is then focused on collisions between a building’s floors and an adjacent building’s columns (floor/column collision). Due to the high frequency content of pounding impacts, the significance of using Timoshenko beam theory instead of Euler-Bernoulli theory is assessed. The shear stiffness in the Timoshenko formulation is found to significantly affect the columns’ predicted performance, and is used in subsequent modelling. An appropriately accurate method of modelling that minimises computational effort is then developed. The simplified model is used to predict the performance of two three-storey buildings that experience floor/column collision. The effects of floor/column impact are predicted for collisions at mid-height, and near the support of the impacted column. Each of these scenarios investigates the effect of building separation on local damage and global damage. Finally, a method to model collision between two adjacent walls that collide out-of-plane is developed (wall/wall contact). The adopted contact element properties are selected using analogous situations that have been previously investigated. The method is used to investigate a single collision between two different wall configurations. In the conclusions, the developed modelling methods from all the considered collision configurations are collected and presented in a summary table. It is intended that these recommendations will assist other researchers in selecting appropriate building pounding modelling properties.