I present a detailed theoretical study of the collective excitation associated with plasmon modes in threedimensional electron gases 3DEG’s, subject to free-electron laser FEL radiations. Using the exact solution of the time-dependent Schro¨dinger equation in which the effect of the electromagnetic e.m. radiation field is included in the Coulomb gauge, I have derived the Green’s function, the density of states DOS, and the density-density correlation function for free electrons in (K,t) and K, representation. With these results, the influence of the FEL radiations on plasmon spectrum in a 3DEG has been studied by employing the randomphase approximation. It has been found that the presence of the linearly polarized terahertz laser fields will lead to a strong modulation of the electron DOS and of the Fermi energy in a 3DEG structure. As a consequence, the plasmon spectrum in an electron gas can be tuned by varying the intensity and/or frequency of the e.m. radiation. A number of important and distinctive effects induced by the FEL radiations are presented and discussed.