Perturbation theory is a collection of methods for the systematic analysis of the global behavior of solutions to differential and difference equations. It is most useful when the first step reveals the important features of the solution and the remaining ones give small corrections. This is illustrated by the solution to the problem of interaction of longitudinal waves in an elastic material with inhomogeneous plane prestrain. The perturbative solution to the governing equation is expanded in a series with a small parameter that characterizes the small strain. The obtained solution that is global in space and time and local in the small parameter is analyzed in detail. Utilization of the solution in practical applications of ultrasonic nondestructive material characterization is discussed on the basis of numerical simulation data.