The optical properties of rod-like two-layer nanoparticles are studied using the notions of equivalent prolate spheroid. The calculations are presented for frequency dependencies for polarizability and the absorption and scattering cross-section of prolate spheroids, cylinders, and spherocylinders. The effect of the sizes, the shapes of the nanoparticle and the material of the core and the shell on the location of the maxima of the imaginary part of polarizability and absorption and scattering cross-sections is analysed. The recommendations regarding the shape and size ratio of the nanoparticles for obtaining the maximum value of radiation efficiency are formulated.