This chapter looks at theory describing vibration fields and relates it to plates and beams that are used to build walls and floors in buildings. An understanding of vibration fields, power input into structures, and sound radiation from vibrating structures is essential to study of sound insulation. The main structural building components for which we need to describe vibration fields are beams and plates. The transmission of sound and vibration involving orthotropic plates is more complex than with isotropic plates, but if the properties in two orthogonal directions are not very different, it is often possible to treat them as isotropic plates. For bending waves this also provides some insight into the vibration field near the boundaries which is more easily obtained for wave propagation in one-dimension (beams) than in two-dimensions (plates). When a beam or plate deforms whilst undergoing wave motion, the internal losses convert vibration energy into heat; therefore high internal losses are desirable for sound insulation purposes.