The 'stack' model of a rate-independent rigid-plastic polycrystalline material is developed. In the 'stack' model, stacks of N neighboring sub-grain domains collectively accommodate the imposed macroscopic deformation while enforcing the velocity and traction continuity condition with its neighbors. The developed 'stack' model is applied to simulate the two-dimensional polycrystalline aggregate under macroscopically imposed plane-strain tension. The effect of inter- and intra-grain interactions on qualitative and quantitative variations in the predicted macroscopic stress-strain response and texture evolution are presented. The diminishing trend of constraint on individual sub-grain domains and texturing rate with stack size N, and saturation for large N also given.