The topic of this thesis are simple statically indeterminate systems. In static analysis of real structures in construction, system analyses are preformed depending on whether the system is statically determinate or indeterminate. The difference between the two systems is in the number of external and/or internal connections; while statically indeterminate have the correct number of links sufficient for geometric invariability, statically indeterminate have at least one link more. The definitions, advantages, and disadvantages of statically indeterminate systems are given at the beginning of the paper. The procedure of determining the degree of static indeterminacy and the procedure for solving indeterminate systems by the force method are presented. The central part includes a continuous beam and the solution of such beam by the Clapeyron equation. The last section describes energy theorems, more specifically Castigliano theorems and their application to the analysis of statically indeterminate systems, and numerical examples of the continuous beam and the application of Castigliano theorems.