The effect of rigid toroidal rotation on the stability of a tokamak to external kink modes is examined. For simplicity a surface current model is assumed. For a high‐&bgr; tokamak it is shown that to leading order the equations governing stability in the presence of rotation are identical to those for a static plasma with &bgr; replaced by &bgr;+S, where &bgr; is the plasma beta andSis a parameter which provides a measure of the rotation rate. For a circular cross‐section tokamak the critical beta for stability to external kink modes in the presence of rigid toroidal rotation is given, to leading order in the inverse aspect ratio &egr;, by &bgr;=0.21&egr;−S. For an elliptical cross‐section tokamak the largest critical beta is obtained for a vertical elongation of 2.2 and is given, to leading order in &egr;, by &bgr;=0.37&egr;−S. The lower limit on the kink safety factorq* or the Mercierqincreases with increase inS. Quantitative estimates of this increase can be obtained from the stability boundaries for the static problem.