A derivation of mathematical model of spatially loaded bars with account of torsion function and transverse shears is considered in the paper. On the basis of the problem, with the use of Hamilton-Ostrogradsky’s principle the variations of kinetic, potential energy and the work of external forces have been determined; and a mathematical model of spatially loaded bars with account of torsion function and transverse shears has been derived. On the basis of the model, the determinant equations of spatially loaded bars have been derived with natural initial and boundary conditions. A sequence of solution of the equations obtained by Hamilton-Ostrogradsky’s variation principle is given in the conclusion of the paper.