A two‐parameter variational model is used to calculate the effects of finite wall thickness on the radial and elliptical stability of cylindrical magnetic domains. The stable region of the (d/h, ℓ/h) plane is found for several values of the dimensionless anisotropy parameter q = Ku/2&pgr;Ms2. As q approaches unity from above, the region grows slightly on the upper side and then begins to contract from both above and below. The model shows a residual stability region down to q ≃ 0.75.