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This work presents estimations of average intragranular fluctuations of lattice rotation rates in polycrystalline materials, obtained by means of the viscoplastic self-consistent (VPSC) model. These fluctuations give a tensorial measure of the trend of misorientation developing inside each single crystal grain representing a polycrystalline aggregate. We first report details of the algorithm implemented in the VPSC code to estimate these fluctuations, which are then validated by comparison with corresponding full-field calculations. Next, we present predictions of average intragranular fluctuations of lattice rotation rates for cubic aggregates, which are rationalized by comparison with experimental evidence on annealing textures of fcc and bcc polycrystals deformed in tension and compression, respectively, as well as with measured intragranular misorientation distributions in a Cu polycrystal deformed in tension. The orientation-dependent and micromechanically-based estimations of intragranular misorientations that can be derived from the present implementation are necessary to formulate sound sub-models for the prediction of quantitatively accurate deformation textures, grain fragmentation, and recrystallization textures using the VPSC approach.