A simple, inexpensive, and fast method of establishing if a defect does or does not exist within a thick-walled solid geometry, which is especially useful to detect if such a defect, a crack, exists within a gun barrel. With further analysis, the method allows not only the identification of the defect's presence; but, a means of establishing the size thereof—which, for example, is critical to understanding if a gun tube has a defect that would warrant its being taken out of service for the safety of its crew or removed from manufacturing. The method involves creating an acoustic vibration in the particular thick-walled, solid geometry, esp. a gun barrel, and observing the vibration pattern which results. The size of the particular defect can be ascertained by a) manually using a correlation between the magnitude of the defect and the relative changes in the decay coefficient or shifts in frequency data or (b) automatically using a Bayes maximum likelihood, statistical pattern classification algorithm and a library comprised of either the decay coefficients or the means and covariances of defect-free and cracked objects.