The onset of natural convection is examined for a fluid‐saturated permeable medium contained between vertical coaxial cylinders of inner and outer radiir*iandr*0. The annular space is of heighth*. The horizontal boundaries are isothermal, with heating from below and cooling from above. Both permeable and impermeable upper boundaries are considered. Critical Rayleigh numbers Racand the preferred convective modes are determined as functons of the geometric ratiosh*/r*iandr*0/r*i. The confining vertical walls of the annular space tend to increase Racabove the value for an infinite horizontal layer. The preferred modes are predominantly asymmetric.