This thesis examines sound transmission through framed and unframed single and double panel systems. The most common example of such a system is a plasterboard double wall. Numerical modelling techniques were used to accurately simulate the motion of the system in response to airborne stimulus. The model was first applied to the simple case of a panel, freely suspended in an anechoic environment. The modelled results were compared to a series of very detailed experimental results, in which many relevant system parameters had been measured. A very good level of agreement was found between the modelled and experimental results for all the system parameters. The model was then applied to the case of a traditional sound transmission loss test for a single panel. The diffuse incident sound field was approximated using a collection of plane wave sources, and the transmitted intensity was calculated directly. The model was seen to give sound transmission loss results which compared very well with experiment. Such a model proved very useful in studying aspects of sound transmission loss which past workers have found difficult to investigate using other approaches. The level of sound transmitted through the panel was seen to be largely invariant with angle of incidence, illustrating that the 'mass law' is not valid for finite panels. The non-resonant transmission of a finite panel was also predicted accurately by modelling a panel which could vibrate in the fundamental structural mode only. The model was used to conduct several parametric studies, which illustrated the effect of changes in mass, stiffness and size on the sound transmission loss of a single panel. The model was also applied to framed double panel systems. Several major simplifications were required to enable an expedient solution to be obtained for these systems, nevertheless the predicted results compared well with their experimental counterparts. Parametric studies showed that there were significant advantages in having cladding of unequal mass on each side of a double wall, due to an associated reduction in resonant transmission. It was also found that smaller walls had higher levels of sound insulation, but this effect was not the same as that associated with decreasing the stud spacing in a wall of constant size.