Experimental uniaxial tensile tests are carried out on circumferential samples removed from annulus tissue of pig intervertebral disks. Classical non-linear and hysteretic mechanical behaviors are observed. Using imaging techniques, the transverse dimensions of experimental samples are measured during stretching leading to the determination of both Poisson's coefficients. A large shrinkage is generally observed in the axial direction while a significant swelling is obtained in the radial direction. This emphasizes the complex coupling effects between the anisotropic fibrous structure and the viscous flow through the matrix. This communication aims at presenting an anisotropic poro-elastic model able to describe the homogenized mechanical behavior (non-linearity, hysteresis) and to retrieve microstructural characteristics (fibers reorientation, coupling with the fluid phase). This characteristic should significantly influences the cell nutrients transport from vertebrae to the disk.