A feasibility study is presented on the experimental application of ultrasound to examine rolled stainless steel plates having equidistant surface textures in two directions in the form of Penrose tiles. The specific problem of interest is investigating surface profile quality in terms of its equidistance and depth to monitor the manufacturing process. The goal is to eventually replace current time-consuming optical examination procedures with a reliable and rapid ultrasonic inspection technique. Two practical experimental setups are discussed and compared in this work: examining frequency spectra obtained from normal incidence pulse-echo measurements, and those obtained at Laue angle incidence. A thorough survey of ultrasonic methods precedes the experimental results to investigate such surfaces from a historical perspective.