The stability of rectangular plates with induced in-plane compressive stresses resulting from the mechanical or thermal loads is discussed in this chapter. The kinematical relations, constitutive law, the equilibrium equations, and the stability equations for a rectangular plate are derived and the classical boundary conditions are presented. The critical buckling loads of rectangular plates under thermal and mechanical in-plane compressive loads are derived and the existence of bifurcation load for each type of given loading condition are discussed. The effect of piezoelectric control on buckling of rectangular plates under thermoelastic loading is investigated. The rectangular plates on elastic foundation under mechanical and different types of thermal conditions namely; the uniform temperature rise and the linear and nonlinear temperature distributions across the thickness of plate, are then considered and the related thermal buckling loads are obtained. Post-buckling and the geometric imperfection of rectangular plates are then followed and the chapter concludes with the discussion on the effect of material temperature dependency on the thermal critical buckling loads.
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