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Although many technologies exist for inspecting piping systems, they are most successful on straight pipes and are often unable to accommodate the added complexities of pipe elbows, bends, twists, and branches, particularly if the region of interest is inaccessible. This paper presents a numerical technique based on the elastodynamic finite integration technique for simulating guided elastic wave propagation in piping systems. Comparisons show agreement between experimental and simulated data, and guided wave interaction with flaws, focusing, and propagation in pipe bends are presented. These examples demonstrate the ability of the simulation method to be used to study elastic wave propagation in piping systems which include three-dimensional pipe bends, and suggest its potential as a design tool for designing pipe inspection hardware and ultrasonic signal processing algorithms.