[en] The paper presents a mathematical model for the calculation of rod structures based on analytical solutions of static and dynamic equations of state for rod or beam elements. Analytical solutions of the equations of state are used in the work and the matrix of influence is constructed from them. The model underlying the calculation allows the use of a real diagram of stretching and compression of structural materials. For a mathematical model, analytical solutions are formed in matrix form. This approach allows us to use the known algorithms of the finite-element and super-elements method for numerical studies and to obtain the result with high accuracy. (paper)