Initial buckling of an elastic coating perfectly bonded to a circular-section prismatic bar subjected to axial extension is investigated analytically. The phenomenon is associated with the substrate Poisson contraction. Two different models of the coating are used: the first is based on classical thin-shell theory and the other is based on first-order shear-deformation shell theory. The results for typical examples are compared and used to explain cracking of the coating previously observed experimentally. © 1993.