Although the study of the interaction of acoustic and elastic waves with periodic surfaces and structures has a rich history dating back to Lord Rayleigh, it has recently been attracting new research efforts due to its value in the study of phononic crystals and in methods for ultrasonic non-destructive evaluation (NDE). The objective of the research described in this thesis is to provide new numerical and experimental tools capable of capturing important features that occur due to the diffraction of ultrasound on periodic solid surfaces. This thesis is divided into four main parts. First, the Rayleigh-Fourier (R-F) method will be used to simulate diffracted fields generated by structures containing multiple periodic surfaces and/or multiple solid layers. The second part of this thesis examines diffraction effects and compares ultrasonic NDE techniques for surfaces with imperfect periodicities. The third portion of this thesis focuses on one unusual phenomenon that has been observed on periodic surfaces, namely the lateral backward displacement of a bounded ultrasonic beam along the surface. This effect is currently understood to occur due to backward propagating surface waves that result from diffraction and mode conversion on the surface. The fourth and final part of this thesis describes the diffraction of bulk ultrasonic waves that can occur on the surfaces of phononic crystals.