Theoretically, we have investigated the propagation of fully and partially coherent flat-topped multi-Gaussian beams through classical and logarithmic axicons. The stationary phase method applied to the Fresnel diffraction integral for intensity distribution has led to applicable relationships. The influences of axicon base angle, beam width, beam flatness, and coherence length with intensity distribution were studied. A number of results have been analyzed and discussed revealing some important conclusions. During this investigation, a specific interest has been given toward producing uniform intensity and long focal depth.