Taking into account the load due to ground displacement and the detachment between a beam and ground, a mathematical model was presented for two kinds of elastic foundation beams under symmetric loads. A kind of beams has a length larger than the width of settlement trough, and another with less length than the width of the trough. Heaviside step function and impulse function were introduced, and their Fourier series expansions were given. According to the established model and making use of the step function and impulse function, an equation set for solving the coefficients of the series that represents the deflection of elastic ground beam was derived. An iteration process to find detachment interval, which is a redundant unknown in the equation set, was put forward. Lastly, verification was done to the proposed series solution by comprising with finite element method. The results show that Fourier series solution is of high accuracy of computation, and can be used as an analytical solution of the elastic foundation beams. To achieve the same accuracy, series solution needs much less amount of calculation. The computed value of detachment interval in the series solution doesn't change with the number of employed series items. In a whole, Fourier series solution offers high accuracy and convenience in dealing with different kinds of loads. It provides an analytical way to effectively solve the problems for an elastic foundation beam under complicated loads.