This chapter introduces the fundamental concepts and solution methods of the energy method and variational principles. The energy method describes mechanical laws in terms of energy variation, while variational principles represent physical laws in a variational form, both transforming elastic mechanics problems into functional extremum problems. It elaborates on the definitions of functionals and variations, calculations of strain energy and complementary energy in elastic bodies, and the minimum potential energy principle, minimum complementary energy principle, and Hamilton’s variational principle. Additionally, it presents two solution methods: the Rayleigh-Ritz method, which assumes displacement functions to solve for undetermined parameters based on the minimum potential energy principle, and the Galerkin method, a representative of weighted residual methods, which obtains approximate solutions by minimizing weighted residuals.