<p>In this paper, we first describe the governing equations and the constitutive relations of a homogeneous isotropic nonlocal elastic medium considering double porosity. Then this mathematical model is applied to investigate the free vibration analysis of an elastic hollow cylindrical solid medium. By applying the time-harmonic variation technique, the governing partial differential equations are converted into a system of ordinary differential equations. The frequency equations for the continuation of vibrations are obtained under traction-free boundary conditions. In order to observe the free vibrations, the frequency equation is further examined using numerical iteration method with the aid of MATLAB software. Graphical representations of the frequency shift against the mode number are presented for both the nonlocal as well as local elastic hollow cylinders with double porous structure using computer-simulated numerical results from the analytical solutions. At the end, various tables are presented to depict the natural frequencies as a function of mode number.</p>