We present a computational spectral factorization method to solve the optimal state feedback control problem for flexible structures with the following features: (1) Mathematically rigorous (2) Wide range of applicability (3) Flexibility of design (4) Fast and Efficient (5) Mini-computer (versus Super- computer) implementation. We apply this method to the following systems: (a) A membrane (b) A string (c) An Euler- Bernoulli/Timoshenko beam models (d) A beam with structural damping and boundary control