A numerical investigation of laminar natural convection heat transfer from small horizontal cylinders at near-critical pressures has been carried out. Carbon dioxide is the test fluid. The parameters varied are: pressure (P), (ii) bulk fluid temperature (T_{b}), (iii) wall temperature (T_{w}), and (iv) wire diameter (D). The results of the numerical simulations agree reasonably well with available experimental data. The results obtained are as follows: (i) At both subcritical and supercritical pressures, h is strongly dependent on T_{b} and T_{w}. (ii) For T_{w} < T_{sat} (for P < P_{c}) and T_{w} < T_{pc} (for P > P_{c}), the behavior of h as a function of T_{w} is similar; *h* increases with increase in T_{w}. (iii) For P > P_{c} and large T_{w} (T_{w} > T_{pc}), natural convection heat transfer occurring on the cylinder is similar that observed during film boiling on a cylinder. The heat transfer coefficient decreases as T_{w} increases. (iv) For subcritical pressures, the dependence of h on D is h ∝ D^{−}^{0.5} in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D^{−}^{0.24}. (v) For supercritical pressures, the dependence of h on D is h ∝ D^{−}^{0.47} in the range 25.4 ≤ D ≤ 100 μm. For larger values of D (500–5000 μm), h ∝ D^{−0.27}. (vi) For a given P, the maximum heat transfer coefficient is obtained for conditions where T_{b} < T_{pc} and T_{w} ≥ T_{pc}. Analysis of the temperature and flow field shows that this peak in h occurs when k, Cp, and Pr in the fluid peak close to the heated surface.