Linear stability of the one‐dimensional flow between infinite vertical coaxial cylinders induced by heating the inner cylinder is considered for various ratios &kgr; of the inner radius to the outer radius, and for Prandtl numbersPappropriate to air and water. For air withP=0.71 the least stable disturbance is nonaxisymmetric for &kgr;<0.44 and is axisymmetric for &kgr;>0.44, and in either case the instability is due to the action of the shear forces. ForP=3.5, the situation is similar, except that the asymmetric shear mode is superceded by an axisymmetric instability driven by buoyancy forces for 0.03<&kgr;<0.16. Wave speeds, wavenumbers, and critical Grashof numbers for these cases and for the case of zero Prandtl number are given.