The nonlinearity generation mechanisms in temperature compensated SAW (TC-SAW) devices arouse great interest recently. Accurate nonlinearity-simulation methods are needed eagerly to predict and further help suppress devices' nonlinearity. This paper develops the propagation theory of finite amplitude waves in nonlinear mediums. The low-frequency variable coupling terms become higher-order nonlinear physical fields' source to derive the third-order harmonic (H3) wave equation. Several important nonlinear origins are taken into full consideration including geometry and material nonlinearity. Based on the nonlinear theory, a nonlinear FEM model is set to directly calculate H3 in TC-SAW resonators without material scale factors, and the bulk mode nonlinear origin is considered with the finite thickness of the piezoelectric substrate. The model explains the periodic bulk wave characteristics of H3 are mainly caused by the nonlinear elastic effect. The amplitude of H3 increases with the thickness of metal and cover layers. Moreover, a new TC-SAW structure with small bumps above the cover layer is designed to suppress H3 response by about 12 dBm.