This thesis will study tamper indicating containers in the context of arms control verification. Verification is an important part of negotiating arms control treaties, as it is necessary to ensure that all parties are in full compliance with the terms and obligations placed upon them. To ensure all parties are compliant verification regimes are required, to this end it may be necessary to ensure that items stored away are not tampered with. To prevent tampering we wish to develop a process that will indicate any attempt at access, even if it is subsequently deliberately hidden. Methods for indicating tampering of containers have been developed that can ensure that a container is not replaced entirely and that the joints of a container are not breached. Our work is to complement the existing techniques by ensuring that the walls of the container are also tamper indicating, to this end we have studied nondestructive guided wave techniques. There are two types of waves, called symmetric and anti-symmetric Lamb waves, that propagate through container walls. These waves travel at different speeds and can be detected separately. When we excite waves, we know how far the slower waves have reached, if we detect these slow waves outside this region it must be due to faster waves scattering into slower modes at a hidden tamper. This technique is easy to use, because at a tamper the slower waves seem to appear out of nothing. We will develop a new method to analyse Lamb wave scattering in plates with abrupt discontinuities, which we will use as a model of a tampered area. The method relies on a precise characterisation of the behaviour of the elastic fields near corners and lead to an accurate and efficient modal representation. Applying this new method to two canonical geometries, a semi-infinite bar and an infinite bar with a step change in depth, we will show how it can improve convergence and accuracy compared to more standard approaches.