A structurally motivated phenomenological constitutive law to describe the anisotropic viscous hyperelastic behaviour of the human posterior cruciate ligament (PCL) at high strain rate is proposed. The mechanical formulation is based on the definition of a Helmholtz free energy function containing a hyperelastic and a viscous potentials which depend explicitly, through tensorial invariants, on the right Cauchy–Green deformation tensor, its rate and a structural tensor characterising the directional properties. The constitutive parameters are identified with experimental data and the ability of the model to capture accurately the key mechanical features of the PCL at high strain rates is demonstrated.