Acoustic resonant modes in a slab with a periodic array of holes are analyzed by using three-dimensional finite-difference time-domain method. We show that there exist two different types of resonant modes in this slab: the coupled Stoneley wave resonant modes and the waveguide resonant modes. Both resonant modes can lead to complex resonant line shapes in the transmission spectrum. By using the distinct property of these resonant modes, a tunable phononic crystal structure consisting of coupled phononic crystal slabs is introduced for achieving acoustic filters and sensors.