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The Discrete Sources Method (DSM) was extended to consider the non-local effect influence of the absorption cross-section of core-shell particle composed of two plasmonic metals. To investigate spectral properties of the core-shell particles the Generalized Non-local Optical Response theory has been incorporated into DSM model. It was demonstrated that variation of metal shell thickness and core diameter as well as elongation of the particle can enlarge the absorption and shift it to the longer wavelength. Besides, it was found that accounting for spatial dispersion leads to decrease the absorption up to 50% of its value with a blue shift about 5-10nm