The propagation characteristics of fiexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The fiexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.