A theoretical model of elastic wave propagation in a cracked porous medium is developed in this paper. When elastic wave propagates through the cracked porous medium, the different physical properties and geometries in different pores structures lead to the fluid pressure gradient in cracks and between cracks and pores. The squirt-flow will take place in two mutually-perpendicular directions, thus, it has anisotropic characteristic. The wave respond contains the crack and background medium permeability information simultaneously. Owing to the fluid dynamic flow process, the effective elastic modulus is complex and frequency-dependent. When the wave frequencies are in high and low limit, the porous medium is elastic. The wave attenuation is obvious and the attenuation is frequency-dependent in the middle frequency region. The anisotropic permeability corresponding to anisotropic characteristic times in the cracked porous medium causes the wave propagation to be affected by the crack connectivity. There appears a second attenuation peak for larger thickness value of crack, meanwhile, and the peak of attenuation is influenced by the thickness value and radius of crack.