The effect of side wall heat transfer on the stability of natural convection in a vertically oriented finite slab of saturated porous material is considered. All six bounding faces are impermeable. A temperature contrast between the top and bottom horizontal surfaces provides the mechanism for destabilization. The narrow vertical end walls are perfectly insulated. The thermal conditions on the broad vertical side walls range from perfectly insulating to fully conducting as determined by the value ofB, the Biot number based on slab height. An asymptotic analysis of the general solution is made in the narrow gap limit &egr;≪1, where &egr; is the cross‐slab width‐to‐height ratio. In this case the relevant heat transfer variable isB¯=&egr;B, the Biot number based on the narrow slab width. In the limit &egr; → 0 whenB¯=O(1), including the caseB¯→∞ that corresponds to a linear side wall temperature profile, tall, vertical, three‐dimensional, finger‐like cells are found at the critical Rayleigh numberRc=&pgr;2/&egr;2. In the limitB¯ → 0 corresponding to perfect insulation, one obtains two‐dimensional,O(1) aspect ratio rolls with axes normal to the side walls at the critical valueRc=4&pgr;2. These two‐dimensional rolls predominate only forB¯=O(&egr;2), and transition to tall narrow three‐dimensional cells occurs whenO(&egr;2)≪ B ≪ O(1).