Examples are shown for analytical solution of engineering structures. The basic procedures for statically indeterminate systems are the force method and the deformation method. The calculation leads to a linear system of equations. The coefficients of the systems are in many cases tridiagonal or one-pair matrices. The solving of this kind of problems is based on a theorem, which states that the inverse of each tridiagonal matrix is a one-pair matrix and vice versa. This enables us to find an analytical solution in numerous particular problems. Examples are taken from theory of reinforced concrete and from different girder and cable-stayed structures.