Conjugate heat transfer in inclined open shallow cavities has been numerically studied. A thick wall facing the opening is heated by a constant heat flux, sides perpendicular to the heated wall are insulated and the opening is in contact with a fluid at constant temperature and pressure. Conjugate heat transfer by conduction and natural convection is studied by numerically solving equations of mass, momentum and energy. The governing parameters were: Rayleigh numbers, Ra from 10(6) to 10(12), conductivity ratio, k(r) from 1 to 60, cavity aspect ratio, A = H/L from 1 to 0.125, dimensionless wall thickness, l/L from 0.05 to 0.20 and the inclination angle, phi from 0degrees to 45degrees from the horizontal. Isotherms and streamlines are produced, heat and mass transfer is calculated. It is found that volume flow rate, (V) over dot is an increasing function of Ra, A, l/L, phi, and a decreasing function of k(r). Heat transfer, Nu is an increasing function of Ra, l/L, and a decreasing function of k(r). A mixed pattern is found with respect to A and phi. In the former, Nu is an increasing function of the aspect ratio up to a critical Rayleigh number, above which the relationship changes and it becomes a decreasing function of A. In the latter case, Nu is a decreasing function at low Raleigh numbers and an increasing one at high Rayleigh numbers.