Experimental data of crack growth rates for various steels were obtained in the near-threshold and the Paris regime at stress ratios with the presence of crack closure (R = 0.1 and R = –1) and for the closure-free stress ratio R = 0.8. Crack closure levels Kcl were derived from the differences between these two curves. The results were much different from the crack closure values computed by the commonly used models by Newman and by finite element analysis even in the Paris regime, where crack closure is usually supposed to be well predicted. The crack driving force in terms of ΔKeff = Kmax – Kcl could not explain behaviour of the investigated materials. Various studied effects (material model, possible violation of small-scale yielding or the effect of specimen thickness) could not explain the differences either. It is unclear whether the intrinsic or the extrinsic resistance to crack propagation was responsible. It means that alternative crack driving force parameters need to be found. Possible ways of finding such parameters will be discussed. Numerical modelling also revealed incorrectness of the commonly used ratio between plastic zone sizes at the free surface and in the middle section of the specimen. It was only about 1.3, in contrast to the classical value of 3.