The purpose of this work is a consistent presentation of the matrix formulation of the Second Order Theory with application in practical analysis and calculation of frame structures. A variational formulation of the Second Order Theory is presented as a special case of general geometric nonlinear analysis. Neglecting the effect of conjugation of axial and transverse deformations (bowing effect), a simplified form of the differential equations of the problem is obtained from general expressions. The stiffness matrices, the geometric matrix and the vector of equivalent forces at the nodes are derived for various cases of boundary conditions at the ends of the rod. As interpolation functions, polynomials and trigonometric (hyperbolic) functions are used, corresponding to the solution of the linearized Theory of the second order. A general computer program has been developed, the application of which is illustrated by several specific examples. The solutions are compared with the corresponding solutions of the general geometrically nonlinear analysis and with the solutions of the classical linear theory.