This paper presents the modeling and numerical simulations of the vibrational behavior of sandwich panels locally overloaded by a fractal distribution of masses. The structural model hypotheses consist in a homogenized material, which is overloaded by small masses distributed following a fractal pattern. The flat panel is then uniformly discretized and the spatial derivatives operators are approximated using finite differences. The time-harmonic equation is recast into an eigenvalue problem and solved to find natural frequencies and mode shapes. The panel is simply-supported on all of its edges. Simulations of a non-overloaded panel are compared to analytic results in term of wavenumbers and mode shapes. Simulations of fractally overloaded panels exhibit localization phenomena when the inter-mass distance is comparable to half the structural wavelength. The influence of the fractal distribution is investigated through the fractal order, the modal frequencies, and the evolution of the modal density. The material is designed to reduce the structural vibration but also the acoustic radiation generated by the structure. The finite differences model can be used to compute the acoustic radiation of such a structure.