With the idea of the phononic crystals, a thin rectangular plate with two-dimensional peri-odic structure is designed. Flexural wave band structures of such a plate with infinite structure arecalculated with the plane-wave expansion (PWE) method, and directional band gaps are found in theΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finitestructure is simulated with the finite element method and verified with a vibration experiment. Thefrequency ranges of sharp drops in the calculated and measured acceleration frequency responsecurves are in basic agreement with those in the band structures. Thin plate is a widely used componentin the engineering structures. The existence of band gaps in such periodic structures gives a new ideain vibration control of thin plates. With the idea of ​​the phononic crystals, a thin rectangular plate with two-dimensional peri-odic structure is designed. Flexural wave band structures of such plates with infinite structure arecalculated with the plane-wave expansion (PWE) method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finites is simulated with the finite element method and verified with a vibration experiment. The frequency frequency of sharp drops in the calculated and measured acceleration frequency response curve are in basic agreement with those in the band structures. Thin plate is a widely used componentin the engineering structures. The existence of band gaps in such periodic structures gives a new ideain vibration control of thin plates.