Effect of wall conduction on free convection across a vertical shallow and square cellular structure is studied to gain improved understanding of heat transfer processes which may provide guidelines for designing and manufacturing cellular materials that have desirable thermal characteristics. Two horizontal walls are insulated and two others are maintained at constant, but different temperatures. The conservation equations of mass, vorticity and energy are solved numerically using finite-difference methods. A two dimensional time-dependent numerical computation method has been developed to determine laminar free convection in closed cavities and conduction in solid walls. Extensive parametric heat transfer calculations have been performed for modified Rayleigh number ranging from 10 4 to 10 8, thermal . conductivity ratio ranging from 2 to 50, Void fraction ranging from 0.25 to 0.49 and Prandtl number ranging from 0.01 to 50. Transient and steady state patterns of stream function and temperature are presented. Nusselt number correlations are presented for square and shallow cellular structure