Abstract:PWM is introduced to calculate the phononic band gaps for two dimensional liquid phononic crystals with square lattices. Complete phononic band gaps are found in the carbon tetrachloride/mercury composite system, and all these band gaps reach the widest point for a filling fraction of ~22%. Among the three different shapes of the inclusions' section studied, the circular section is easier to attain large band gaps than the square section and obliquely rotated square one. The widest band gap ΔΩ=0.5497 appears in the circular section system when the filling fraction f=0.229. If the substances of the inclusions and matrix are interchanged (i.e., mercury/carbon tetrachloride system), the gaps obtained are much narrower.