The article deals with the rod model for the analysis of stress-strain state of rod structures. Analytical solutions are obtained by the operating method. It is assumed that the rod elements can have variables along their axis of physicals characteristics. External loads can also vary along the axes. Calculation formulas are suitable for loads distributed according to an arbitrary law. Unlike the finite element method, defining matrices are formed after obtaining an expression, allowing to calculate the nodal forces through nodal displacements. Examples are given to demonstrate the accuracy of the obtained expressions.