In the article the variation method of calculation of the loaded statically indeterminable structures strengthened by increasing the section of elements and the constructive and design model of structures modifying by installation of additional elements is presented. The procedure of the stress-strain state of the strengthened loaded structures determining, taking into account the repair and mounting stresses and also attached additional elements is presented. Computer program, which is based on the described methodology and allows to simulate the strengthened structure and to determine its stress-strain state at various stages of considering the deformation and stress during the current action of strengthening is composed. Reliability and high accuracy of calculations made by this program are established by comparing them with the data of test examples and solution problems, which were obtained by other methods.