Galerkin's method, concept of variational derivatives, review, dynamical-elastic problem with boundary conditions, equivalence of principles and respective equations, set of generalized equations of Ritz for Beck's rod, stability, Other numerical methods in solid mechanics, Newton-type methods, surveys, Hamilton's principle, principle of virtual work, Beck's clamped rod, non- self-adjoint problems, convergence problem, Rods (beams, columns, shafts, arches, rings, etc.), Variational principles of physics, Plates, Rayleigh-Ritz method, plate with simply supported, or clamped or free parts of boundary contour