Using the biphasic theory for hydrated soft tissues (Mow et al., 1980) and a transversely isotropic elastic model for the solid matrix, an analytical solution is presented for the unconfined compression of cylindrical disks of growth plate tissues compressed between two rigid platens with a frictionless interface. The axisymmetric case where the plane of transverse isotropy is perpendicular to the cylindrical axis is studied, and the stress-relaxation response to imposed step and ramp displacements is solved. This solution is then used to analyze experimental data from unconfined compression stress-relaxation tests performed on specimens from bovine distal ulnar growth plate and chondroepiphysis to determine the biphasic material parameters. The transversely isotropic biphasic model provides an excellent agreement between theory and experimental results, better than was previously achieved with an isotropic model, and can explain the observed experimental behavior in unconfined compression of these tissues.