Numerical solutions for laminar natural convection in a vertical shrouded fin array are presented. Analysis of a physically realizable configuration is compared to published results for an adiabatic shroud. The effect of a uniform heat flux on the heat sink shroud representing an incident solar heat load is also examined for a vertical heat sink with natural convection and radiation. Comparison to closed form relations for laminar flow between plates lends some insight into the influence of the developing boundary layer on the heat sink thermal performance. Some heat transfer enhancement beyond that of an adiabatic shroud was observed at high Grashof numbers. At low Grashof numbers the Nusselt number was lower than for an adiabatic shroud. However, compared to no shroud, the presence of a shroud at any distance from the fin tip improved the transfer of heat from the fin array. The benefit of the shroud when a heat load is present appears to be greatest for a shroud clearance of C = 0.5 to 1.0.