This book is to propose different beam models for static, buckling and vibration analysis of functionally graded isotropic and sandwich beams embedded in hygro-thermo-mechanical environments. It composes of six chapters in which improved first-order and higher-order shear deformation beam theories are developed to investigate effects of both transverse shear and normal strains on the static, buckling and vibration responses of the beams. Moreover, in order to investigate the size effects of functionally graded micro- and nano-beams, the modified couple stress theory and Eringen's nonlocal elasticity theory are used. In addition, Navier, Ritz and finite element methods are also developed to invesitate effects of the material distribution, thickness ratios of layers, slenderness and boundary conditions of the beams under different configurations of hygro-thermo-mechanical loadings.