A numerical finite elements investigation has been conducted to determine the effects of Rayleigh number Ra, eccentricity E, angular position γ, and radii ratio R1R0 on the laminar natural convection of air between horizontal isothermal concentric and eccentric cylinders. Temperature profiles, stream function profiles and heat transfer rate have been computed for radii ratios of 0.1 to 0.9, Rayleigh number from 103 to 8×105, eccentricity E from 0.1 to 0.5, and angular positions γ from 0° to 360°.