Under the terms of the Creative Commons Attribution (CC BY) license to their work. ; Hypersonic, thermally activated surface acoustic waves propagating in the surface of crystalline silicon patterned with periodic stripes were studied by Brillouin light scattering. Two characteristic directions (normal and parallel to the stripes) of surface acoustic waves propagation were examined exhibiting a distinctive propagation behavior. The measured phononic band structure exhibits diverse features, such as zone folding, band gap opening, and hybridization to local resonance for waves propagating normal to the stripes, and a variety of dispersive modes propagating along the stripes. Experimental results were supported by theoretical calculations performed using finite element method. ; The authors acknowledge the financial support from the FP7 FET Energy Project MERGING (Grant No. 309150); the Spanish MICINN projects nanoTHERM (Grant No. CSD2010-0044) and TAPHOR (MAT2012-31392). N.K. acknowledges support from the Micro and Nano Systems Center of Excellence - IMEL/NCSR DEMOKRITOS. ; Peer Reviewed