The article is devoted to the development of mathematical dependence of determination the natural oscillation frequencies of reinforced concrete span structures according to the physical, mechanical, geometric and energy characteristics of their elements and materials. Carrying out and processing the results of the experimental studies as well as the analysis of literature revealed the ways of reducing the error of the existing mathematical dependences in determining the natural oscillation frequencies of the span structures. The use of Griffith’s energy approach, the account of the nonlinear law of stiffness changes and the subsequent approximation of the experimental data made it possible to reduce the error of the mathematical dependence in the process of determination the natural oscillation frequencies of span structures by 4.4 times. The effect obtained makes it possible to apply the developed mathematical dependence to monitor the technical condition of the reinforced concrete span structures and the numerical determination of the boundaries of their technical condition categories.