A fast model of roll stack deformation is presented. Appropriate simplified structural models are chosen by careful consideration of the application of general theories. Discretization of continuous variables allows the use of matrix-based weighting functions in describing component deformation and leads to a vectorized solution. All model non-linearities are considered, with particular attention given to the variable region of contact between adjacent rolls in the stack. A novel and efficient ‘binary choice matrix’ method is developed to describe the uncertainty in defining this region. This leads to a more efficient solution than previously published related models. Opportunities for future extensions are discussed.