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The fracture behaviour of concrete subjected to mode I crack openingunder low-cycle loading was investigated. Two widely accepted non-linear methodswere used: the Cohesive Crack Model to analyse the evolution of the process zoneand the Continuous Function Model (CFM) to analyse the local hysteresis loop un-der unloading-reloading. In the original formulation, the CFM assumes that thetension-softening law is independent of the number of cycles and that no damageoccurs during the so called inner loops. The above mentioned hypotheses entail anunrealistically high endurance limit. A more realistic behaviour of the numericalmodel is obtained by rescaling the tension-softening law with the number of cycles.The numerical results obtained by varying the size ratio and keeping all other geo-metrical and mechanical dimensionless parameters constant show that the endurancelimit is an increasing function of size.