The polyurethane, which was the subject of the constitutive research presented in the paper, was based on oligocarbonate diols Desmophen C2100 produced by Bayer?. The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses. The polyurethane was assumed to be non-linearly viscohyperelastic, isotropic and incompressible. The constitutive equation was derived from the postulated strain energy function. The elastic and rheological constants were identified on the basis of experimental tests, i.e. relaxation tests and monotonic uniaxial tests at two different strain rates, i.e. λ= 0.1 min-1 and λ= 1.0 min-1. The stiffness tensor was derived and introduced to Abaqus?finite element(FE) software in order to numerically validate the constitutive model. The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material. The polyurethane, which was the subject of the constitutive research presented in the paper, was based on oligocarbonate diols Desmophen C2100 produced by Bayer ?. The constitutive modeling was performed with a view to applying the material as the inlay of intervertebral disc prostheses. The polyurethane was constitutively be be non-linearly viscohyperelastic, isotropic and incompressible. The constitutive equation was derived from the postulated strain energy function. The elastic and rheological constants were identified on the basis of experimental tests, ie relaxation tests and monotonic uniaxial tests at two different strains rates, ie λ = 0.1 min-1 and λ = 1.0 min-1. The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyu rethane material.