It is widely admitted that the understanding of the recrystallisation process requires an accurate description of the mechanical response of the polycrystalline aggregate. Indeed, numerous factors necessary for a correct description of recrystallisation originates from microstructural characteristics which result from a mechanical loading. Among others, one can cite the crystallographic texture, the density and the distribution of dislocations, the stored energy, the intragranular misorientation, the strain heterogeneity etc... To estimate some of these microstructural features, a mean-field polycrystalline approach based on the self-consistent scheme has been used previously [1] and further developments have been proposed to introduce the notion of intragranular heterogeneity [2]. One aim of the present paper is to recall the potentiality of the mean-field approach (MFA) concerning the statistical description of the local mechanical fields. Especially, it is recalled that it does contain an information on their fluctuation within a constitutive phase, i.e. ensemble of grains with a given crystalline orientation. Different mean-field approaches (the Taylor model and two self-consistent schemes) are then used to estimate the mechanical response of a copper polycrystal, namely the crystalline texture evolution and the intracrystalline hardening. For that goal, the parameters of the local behaviour (constitutive and hardening laws) are first identified on experimental macroscopic responses for shear and tensile loadings, and the different models are used to predict the mechanical state after a rolling deformation in terms of dislocation density distribution, texture and strain rate intraphase heterogeneity. The trends obtained with the different models are discussed.