Use of the deflection expression of an infinite plate subjected to a concentrated force in connection with the method of images permitted solutions for a wedge-shaped plate, infinite strip, semi-infinite strip, and rectangular plate simply supported along their edges. The closed-form solutions that were obtained for the semi-infinite and rectangular plate were evaluated and the results reveal that, in the rectangular corner plate, the corner reaction is negligible for λr0≥5. It was also found that, for λr0 <4, in the corner area there appear negative bending moments which by far exceed the absolute maximum value of the negative moment of an infinite plate. The solutions of the infinite strip, semi-infinite strip, and rectangular plate were obtained as infinite series of fundamental deflections. It is noted that the series for deflections, moments, and shear forces converge rapidly, particularly in the vicinity of the concentrated forces. Advantages in using superpositions of fundamental deflections, as compared with using Fourier-type series, are noted in treating the infinite plate subjected to arbitrary loads.