The problem of natural convection of a non-Newtonian power-law fluid with or without yield stress about a two-dimensional or axisymmetric body of arbitrary shape in a fluid-saturated porous medium is analyzed on the basis of boundary layer approximation. For a high modified Rayleigh number, similarity solutions are obtained by using the fourth-order Runge-Kutta scheme and shooting method for two-dimensional bodies without yield stress and a cone with yield stress. The effects of the surface heat transfer rate q(w)(X), the local Nusselt number Nu(x), the overall heat transfer rate Q* and the power indices n of fluids with the yield stresses on the free convection heat transfer characteristics are discussed. It is found that the results depend strongly on the high values of the yield stress parameter Omega/a at the boundary.