The lateral surface of a cylindrical structure, which is composed of a thin tube embedded in a large outer medium, is submitted to a uniform external pressure. The buckling pressure of such a structure, corresponding to a low flexural state of the inner tube wall, is theoretically analyzed on the basis of the asymptotic method. The theoretical results are compared with experimental ones obtained from a compression test realized on an elastic tube inserted in a foam. It is found that the Euler pressure and the associated buckling mode index strongly depend upon the rheo-logical and geometrical parameters of both the tube and the surrounding medium.