Six classes of the stack were recently introduced for describing the system change pathway under varying environment or events “on and above” the normal situations. Not only can stack store items at the top, but also can store items at the bottom, side(s), as outer ring, inner ring or randomly. The purpose of this paper is to develop the mathematical foundations and their programming algorithms for the necessary handling of the insertion and deletion operations in each of six generalized stacks. A Generalized Data Stacking Programming (GDSP) model is proposed to simulate what happen in the real world. GDSP uses the growing/shrinking matrix based implementation which is a generalization of the known array representation to be another way of implementing the stack.