The traditional Green's function has been widely used to analyze surface acoustic wave (SAW) devices for many years because of its physical basis and its ability to model many propagating modes. Simplifications are, however, introduced in the derivation of the traditional Green's function that cause it to ignore some important effects, such as mass loading caused by surface electrodes. Recently, a generalized Green's function was introduced that is able to include mechanical loading effects. Based on previous work by E.L. Adler (1994) and R.C. Peach (1995), we use concise matrix notation to deduce the generalized Green's functions that describe the effects of surface stresses and electrical displacement on the three mechanical displacement components and on the electrical potential. Effective permittivities of 15 materials/cuts and the 16-element Green's functions for two materials are presented.