Slow crack growth (SCG) behaviour has been investigated under creep conditions in a medium density ethylene-butene copolymer (MDPE) on both axisymmetrical Full Notched Creep Tensile (FNCT) and Double Edge Notched Tensile (DENT) samples tested at 60 °C. An attempt is made to predict the long-term failure of a component under creep loading conditions, using an incremental damage law. The experimental creep damage observations were compared to the creep stress-strain distributions calculated by finite element method. Such comparison can provide a damage evolution law as a function of the maximum principal stress and the creep strain. The failure criterion is expressed in terms of a critical creep damage over a critical distance. This model is applied to creep crack growth on the FNCT and DENT samples.