We propose a mechanical model to describe the “quasi-elastic” stress-strain relation for soft biological tissues, based upon their fibre structured design. The corresponding elastic constitutive equation is derived and we show how the model parameters may be calculated to fit the model to experimental data. Some examples of such fittings are given for different materials such as human vein, fascia, tympanic membrane and rabbit papillary muscle. The good quality of these adaptations illustrates the multiple application possibility of the proposed model.