High stress in a crucial instrument part can cause failure. Stress detection is one of the aims of nondestructive testing. The velocity change of acoustic waves can be used to detect stress in a material. An acoustic microscope is an instrument which induces and detects acoustic waves and in one mode of operation, is able to measure the velocity of acoustic surface waves. It does this over a very small area and is capable of high spatial resolution;One of the challenges in the measurement of stress is the achievement of high spatial resolution. Since the stress induced velocity shifts are generally small (~0.01%), the required precision of time and distance measurements can be quite high for the short propagation distances required for high spatial resolution. The goal of this dissertation is to measure residual stress via the acoustic wave velocity with spatial resolution on the order of one millimeter or less;There are many types of acoustic waves. The type of interest here are surface waves known as Rayleigh waves. The velocity of these waves are determined by time and distances measurements. The high precision necessary leads to many complications in the measurements. These are described and, for a few cases, overcome;The sound velocity in a material can be used to describe material characteristics other than stress. The instrument was used to measure the velocity of Lamb waves on freestanding diamond films. The possibility of using these velocity measurements as a method of characterizing the diamond films is explored. Attempts at using the acoustic microscope on a variety of materials with a large range of Rayleigh wave velocities led to the discovery of surface waves following the second and third front surface reflections between the lens and the surface of the sample. The explanation of these surface waves and their uses are described;Velocity measurements were made on a sample of silicon carbide during loading in an attempt to measure applied stress. Shifts in the velocity were observed but were not reproducible. The problems with these measurements are described and some possible causes given.