Many engineering structures are regular in form, with repeating cellular units across which it is necessary to be able to predict bending and in-plane wave transmission. Such structures often exhibit features such as high propagation losses, tunneling and spatial filtering. Using validations against measurements and finite element modes, examples are shown for finite, periodic plate and beam structures demonstrating that prediction of wave transmission using Advanced Statistical Energy Analysis (ASEA) can be significantly more accurate than SEA as it is able to account for these features by incorporating ray tracing.