Exact solutions are developed for small Rayleigh number free convection in 2-dim. porous cavities of various shapes due to a uniform temperature gradient normal to the gravitational field. The theorem is established that such flows are independent of cavity orientation. The appropriate (rotation-invariant) characteristic length is thus A 1 2 (A, cross-sectional area). Exact solutions are presented in detail for rectangular and elliptical cavities with λ (ratio of long to short axis) arbitrary, and for equilateral triangular cavities. The critical Rayleigh number for applicability of the analysis is about 1 for cavities with long axis horizontal, and about λ 2 with long axis vertical. Simple exact solutions exist also for cavities of other shapes.