The viscoplastic behaviour of a medium density ethylene–butene copolymer (MDPE) is investigated by using samples cut out from thick-walled MDPE pipe. Extensive experimental work has been performed to characterise the nonlinear time-dependent response of such semi-crystalline thermoplastic material. Tests were carried out at 60 °C, on smooth tensile, full axisymmetrically notched creep tensile (FNCT) and double edge notched tensile (DENT) specimens. Tests were conducted under constant strain rate, creep, stress relaxation and dip-test conditions. The experimental data on smooth uniaxial specimens indicate two regimes of creep deformation as well as the existence of a back stress effect. The notched geometries allowed to investigate the creep behaviour of a structure with a local multiaxial stress states near to the crack tip. In order to model the observed material behaviour, a double inelastic deformation model, DID, containing two additive inelastic mechanisms is suggested. Both DID model and its parameters' optimiser are already implemented in the F.E.M. Zset code at Ecole des Mines de Paris. It is shown that this model is able to reproduce the creep strain history on homogeneous uniaxial tensile tests in a large range of strain rate including the back stress effects, as well as on cracked specimens. Moreover, the time dependent multiaxial stress–strain fields computed (under finite strain formulation) in the vicinity of the crack tip are in good accordance with the Riedel and Rice (RR) analytical singularities. Thus, this fully predictive model clearly shows its superiority and effectiveness over models that take into account only one inelastic viscoplastic deformation under uniaxial conditions.