The wave transmission in different arrayed structures with different media and different frequency domain was calculated. It is found that the self-collimation effect of wave can be found in the designed arrayed structure phononic crystals being similar to the self-collimation of light in photonic crystals. Further computations show that the wave self-collimation can be related to the designed media and the material properties in the arrayed structures. Moreover, this phenomenon can be also affected by the geometrical property of the cross section of the metal pillar in the arrayed structures. The frequency domain for the self-collimation effect of wave increases initilally and then decreases with the increase of the specific modulus, and it is decreased with the increase of the specific density. The optimal designs on specific modulus, specific density and the geometrical properties are the key factors to realize the controlling of frequency domain of the wave self-collimation effect in the arrayed structures. Equi-frequency contour is the key criterion for the design of the self-collimation effect of wave in the periodic arrayed structures.