This chapter presents buckling and post-buckling analysis of straight beams under thermal and mechanical loads. The Euler and Timoshenko beam theories are considered and buckling and postbuckling behaviors are discussed. The buckling analysis of beams with piezoelectric layers is presented and the effect of piezo-control on the beam stability is analyzed. The vibration of thermo-electrically excited beams in the state of buckling and post-buckling is discussed and the chapter concludes with the thermal dynamic analysis of beams. The beam material in this chapter is assumed to be functionally graded, where the presented formulations may be simply reduced to the beams with isotropic/homogeneous material.