Metal nanoparticles (NPs) distinguish themselves from other nanostructures by their unique surface plasmon resonance (SPR). This work focuses on a comprehensive investigation into the plasmonic resonances of core-shell nanospheres composed of gold (Au), silver (Ag), and aluminum (Al) cores, and shells composed of different materials through numerical modeling using the finite element method (FEM) implemented in COMSOL Multiphysics. Core-shell NPs have unique optical properties for various applications, including sensing and imaging. Through numerical simulations analyzing the scattered field of nanospheres, this study systematically examines the effects of core and shell materials at different sizes, refractive indices of the surrounding media, and thicknesses on SPR modes and wavelengths. The findings indicate that the SPR of Au, Ag, and Al nanospheres occurs in the infrared (IR), visible, and ultraviolet (UV) portions of the electromagnetic spectrum, respectively. The resonance sharpness showed Ag NPs with more intense and sharper plasmonic resonance compared to Au NPs. Key findings demonstrate that the refractive index of the shell red-shifts the localized surface plasmonic resonance (LSPR) wavelength and decreases normalized absorption cross-section (Qab). An increase in the shell's thickness results in an increase in LSPR and Qab. The extinction coefficient (k) is shown to have an inverse relationship with LSPR wavelength, resulting in a blue-shift and a decrease in Qab. By systematically investigating material parameters for core-shell structures, this study aims to develop an understanding of suitable ranges for sensing, focusing, and heating applications.