In the previous report, general description on the influence functions of a given plate and their application to plate problems was indicated. Then two classes of new influence functions are introduced and their fundamental relations are discussed. The method of application of those new influence functions to initial stress problems of infinite as well as semi-infinite plates were illustrated. In this report, influence functions for deflection of a rectangular plate are derived first for two different cases of boundary conditions, and newly introduced influence functions of the plate under concentrated hydrostatic pressure and couple are determined. From these functions, influence functions for infinite plate strips of two different boundary conditions are derived and application of these functions to initial stress problem are illustrated with numerical examples.