The aim of the model is to describe the temporal behaviour of cumulative seismic moment released in aftershock sequences. It therefore constitutes an alternative approach with respect to the Omori and Utsu laws, which model the number of events against time. Static fatigue is assumed to be the principal explanation of the aftershock temporal behaviour; as a result, aftershocks can originate at a stress intensity factor lower than the fracture toughness. Under the condition that the mainshock causes a redistribution of stress, the initial stress condition of the aftershock sequence at mainshock origin time t 0 can be considered as the superposition of the stress before the mainshock and of the stress step dσ caused by the dynamic rupture of the mainshock. The model can be written in the form: S(t) = dσ + (RTγ)ln t, where S(t) is the cumulative stress drop at time t after the mainshock, T the temperature, R the universal gas constant and γ a constant dependent on material type. The model is derived from the empirical static fatigue law t = s exp[(U - γσ)RT], widely applied in fracture mechanics (σ is the stress, s a constant and the other parameters as above). The fit of the model to five aftershock sequences, obtained by linear regression analysis, is quite good with the r 2 greater than 0.85 for all the sequences, but the Imperial Valley sequence where r 2 = 0.7. The results seem to favour the hypothesis that the decay of the rate of seismic moment release depends on temperature, in agreement with other evidences based on the evaluation of the decay rate of Omori law, but in contrast to some static fatigue results obtained in laboratory tests on granite rocks. The scarcity of field data on underground temperature does not allow any definitive conclusion about this subject.