A simple and general new approach to predict deformation texture evolution during large plastic strains is presented. The stress in each grain, first calculated by a Taylor model, is then modified by the stresses of adjacent grains thereby making the local slip systems and lattice rotations neighbour dependent. Examples of texture simulations during hot rolling of aluminium alloys are given. The model predictions are compared with the standard Taylor model predictions and with ODF data of the textures measured during hot plane strain compression.