Noise and vibration are important design issues for many types of vehicles such as ships, cars, and aeroplanes. Structure borne sound, which may be of relatively high frequency, usually emanates from an engine or some other type of localised source and propagates through the vehicle. Excessive vibration levels, and thus structural damage, may occur while structural acoustic interactions may lead to unacceptable interior noise. In the analysis of energy transmission between plate structures, it is common practice to consider only bending modes (or waves) of the structure. However if the concern is with high frequency vibration analysis, then due allowance may need to be made for the presence of inplane shear and longitudinal modes. Due to the infeasibility of the industry standard technique, the Finite Element Method, at high frequencies, almost all of the studies that have investigated the importance of in-plane energy transmission have used Statistical Energy Analysis (SEA). In this study an existing dynamic stiffness method is extended to include in-plane effects, and used as a benchmark against which SEA is assessed. Additionally the Wave Intensity Analysis (WIA) technique, which is an improved form of SEA, is extended to in-plane vibrations, and used to identify some of the reasons for the poor performance of SEA in certain applications. All three methods are applied to a wide range of plate structures within the frequency range of 600 Hz to 20 kHz. While the response levels as predicted by the WIA are generally quite close to exact results, it has been found that although all of the requirements which are usually postulated for the successful application of SEA are fulfilled, SEA severely underpredicts the energy transmission in large structures because of the diffuse wave field assumption. It is also shown that the exclusion of in-plane modes may lead to sizeable errors in energy predictions unless the structure is very simple.