The paper treats the stability of surface waves generated when a rubber half-space is subjected to compression. At a load level below the critical one an asymptotic expansion is given for the difference between the potential energy of an adjacent state and that of the fundamental state. The displacement field is expressed approximately by a linear combination of two different buckling modes and a residual displacement field which is orthogonal to the former fields. This remainder permits us to take into account the effect of all other modes which have been neglected. The wavelength of the two modes are governed by the dominant imperfections of the half-space. Terms up to the fourth order in the amplitudes of the buckling modes are included.
Results are presented to show the most severe post-buckling behaviour as presented by the line of steepest descent in the load displacement diagram. Furthermore curves showing the reduction of the critical load on account of the imperfections in the two dominant modes are also presented. The analysis is kept sufficiently general to include the effect of pre-straining the rubber half-space upon the post-buckling behaviour.