Abstract: Nonlocal constitutive models are widely used for effectively simulating strain localization. The major models may be classified into the following two kinds: the weighted-area-averaged nonlocal model and thegradient-enhanced-nonlocal model. Comparison between the two models ismade in this paper. It is found that the Aifantis model is a reasonable choice fornumerical simulation of a localized non-homogeneous material, but it issubject to some improvements.