Ground-borne vibration has existed ever since the development of urban road and rail networks. Vibration generated by the moving traffic propagates through the ground and into buildings, resulting in unacceptable levels of internal noise and vibration. A common solution to this increasingly significant problem is the base-isolation of buildings by incorporating vibration isolation bearings between the buildings and their foundations. This technique has been employed for over forty years but the exact performance of base isolation remains uncertain. This dissertation is concerned with the development of a generic computational model; generic in that it accounts for the essential dynamic behaviour of a typical base-isolated building in order to make predictions of isolation performance. The model is a linear one, formulated in the frequency domain, and consists of a two-dimensional portal-frame model of a building coupled to a three-dimensional boundary-element model of a piled-foundation. Both components of the model achieve computational efficiency by assuming they are infinitely long and using periodic structure theory. The development of the model is described systematically, from the modelling of a building and its isolation bearings to that of its foundation. The majority of the work is concerned with the piled-foundation model, which is comprehensive in that it accounts for the vertical, horizontal and rotational motion of the pile heads due to both direct pile-head loading and interaction through wave propagation in the surrounding soil. It is shown that this level of detail is important in the prediction of base isolation efficiency. A key question facing designers is not only how but on what basis base isolation should be assessed, since fundamental problems exist with the existing measures of isolation performance. Power flow analysis is explored and the concept of power flow insertion gain, based on the total mean vibrational power flow entering a building, is introduced as a useful measure of isolation performance. This is shown to offer clear benefits by providing a single measure of performance that is suitable for design purposes. Finally, the development of a prototype force-sensitive vibration isolation bearing is described as a contribution to verifying base-isolation theory with experiments.