A couple of years ago, one of the authors presented a paper entitled “On the Influence Surfaces of Orthotropic Plates” and last year he has also puplished another report on the same subject from his research institution. His studies so far has been concentrated to the design problems of orthotropic plates under lateral loading. Through his recent study on the thermal stress problems of plates, however, he has found that use of various influence functions of plates will be very effective in research on the initial stress problems of plates such as residual stresses and thermal stresses. In this report, two classes of new influence functions are introduced and their fundamental relations are discussed. With several simple examples, the method of application of those new influence functions to initial stress problems will be briefly indicated.