Abstract. This paper presents the Green's function for a uniform thin beam which is assumed to obey the Euler-Bernoulli theory at resonant condition. The beam under study has a simple support at one end and a sliding support at the other. First, the differential equation governing the free vibration of the beam is obtained in the frequency domain using the Fourier transform. Then, we try to find the corresponding Green's function of the problem. But a contradiction occurs due to the special properties of resonance. In order to overcome this hurdle, the Fredholm Alternative Theorem is utilized. Remarkably, it is shown that this theorem, by adding a particular term to the Green's function, can remedy this problem and the modified Green's function is consequently established. Moreover, the deformation function of the beam is found in an integral equation form. Some diagrams and tables conclude this study. of a Timoshenko beam and multi-mass oscillators. He showed that in the case of the beam with a spring-mass system attached, the frequencies of the system lower than the spring-mass frequency are decreased, and the higher ones are increased (except at discrete points when the frequencies are unchanged).Soon after, Foda and Abduljabbar [4] presented an exact and direct modeling technique based on the dynamic Green's function for the modeling beam structures subjected to a mass moving at constant speed. The equation of motion in the matrix form was formulated and was non-dimensionalized, so that the numerical results presented are applicable to large combinations of system parameters. A method of determining the dynamic response of uniform damped Euler-Bernoulli beams subjected to distributed and concentrated loads was presented by Abu-Hilal [5]. Also Green's function for various beams with different boundary conditions were given.Moreover, the use of the static Green's function in engineering mechanics is common. For instance, Failla and Santini [6] revealed that uniform-beam static Green's functions can be used to build efficient solutions for beams with internal discontinuities due to along-axis constraints and flexural-stiffness jump. The equilibrium equation was derived in the space of generalized functions, and the original bending problem was recast as linear superposition of a principal and an auxiliary bending problem, both involving a uniform reference beam and homogeneous boundary conditions. Later on, Failla [7] presented a solution using static Green's functions for Euler-Bernoulli arbitrary discontinuous beams acted upon by arbitrary static loads. For stepped beams with internal springs, a closed-form solution was proposed, while for stepped beams with internal springs and along-axis supports, the solution was given in terms of the unknown reactions of the along-axis supports, which could be computed based on pertinent conditions. It is worth mentioning that Azizi et al. [8] used the spectral element method in frequency domain to analyze continuous beams and bridges subjected to a moving load. They util...