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The influence function for the deflection of a simply-supported plate having the form of an equilateral triangle has not yet been found in literature, although some methods of solution were suggested by several authors. The main difficulty is that the operations and calculations involved in these suggested methods are too complex and cumbersome to be carried out in practice. In this paper the influence function as mentioned above is successfully obtained by using the method of images in a special manner that reduces our problem to the static problem of a rectangular plate, the solution of which can be worked out without difficulty. The result is described by the double trigonometrical series which is presented in a very simple form. The stability and vibration problems of an equilateral triangular plate simply supported at the edges are also discussed in this paper by taking advantage of the influence function just obtained. Our results completely coincide with those obtained by other authors taking different ways of approach.