This paper describes a fast and parallel stack-based linear genetic programming system for local contact search algorithms of finite element impact analyses. Here the present GP system is used to find the function approximating local coordinates of the contact point in the local contact search process of the master-slave type contact algorithm. The proposed system is superior in computing speed and in accuracy of finding approximating function than the pointer-based GP system which was proposed by the authors in the previous paper. The fundamental formulation of this system is first described in detail, and then its basic performance is demonstrated through some sample analyses on a PC cluster.