A state space procedure for the formulation and solution of the mixed boundary value problems is established. It is a natural extension of the method used in the initial value problems : however, certain special theorems and rules should be developed. The scope of the applications of the approach includes the beam,arch, axisymmetrical shell problems in structural analysis, boundary layer problems in fluid mechanics and eigenvalue problems for deformable bodies, etc. Many classical methods in these fields developed by, for example, Holzer, Prohl, Myklestad, Thomson, Love-Meissner, etc. can be either simplied or unified under new light shed by the state variable approach. A beam problem is included as an illustration.