Weakly nonlinear analysis is used to calculate the possible two‐ and three‐dimensional convection patterns in a rectangular parallelepiped of saturated porous media when the horizontal dimensions are integral multiples of the vertical dimension. A two‐term expansion for the Nusselt number is found for values of the Rayleigh number close to the critical values. It is shown that the two‐dimensional roll configurations transfer heat more effectively than does the three‐dimensional pattern of motion when the Rayleigh number is just above the critical value.