The degradation of railway tracks can be observed through several measurement techniques. Recently, a method to diagnose the railway track using Fiber Bragg gratings (FBG) has been proposed. FBG are integrated inside the railway sleeper and is named a "Smart Sleeper". To study the sleeper behavior, an analytical model for the dynamics of railway sleepers has been developed, which can calculate rapidly the sleeper responses. In this model, by using the relation between the rail forces and displacements of a periodically supported beam, the dynamic equation of the sleeper is written with the help of the Euler-Bernoulli beam equation and Dirac's functions. Subsequently, thanks to the Green's function of this system, the sleeper dynamic response is calculated analytically. A linear relation between the train loads and the sleeper strains is shown in the frequency domain. This article presents an application of this model to calculate the train loads from the strains measured by the FBG. Based on the analytical model, we obtain a matrix which presents the link between the loads and the sleeper responses. By integrating this matrix and the Fourier transform of the measurements recorded by the FBG at the middle and at the two rail-seats, the train loads can be quickly calculated by using the solver mldivide of MATLAB. The numerical application shows that the identified train loads are different for different wheels and different rails. This highlights the irregularity of the wheel-rail contact forces which can be used to detect the defaults in the rolling stock in future works.