A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near its cut-ofi frequencies is derived. Leading order solutions for dis- placement and pressure are obtained in terms of the long wave amplitude by direct asymptotic integration. A governing equation, together with corrections for displace- ment and pressure, is derived from the second order problem. A novel feature of this (two-dimensional) hyperbolic governing equation is that, for certain pre-stressed states, time and one of the two (in-plane) spatial variables can change roles. Although whenever this phenomenon occurs the equation still remains hyperbolic, it is clearly not wave-like. The second order solution is completed by deriving a reflned governing equation from the third order problem. Asymptotic consistency, in the sense that the dispersion relation associated with the two-dimensional model concurs with the ap- propriate order expansion of the three-dimensional relation at each order, is verifled. The model has particular application to stationary thickness vibration of, or transient response to high frequency shock loading in, thin walled bodies.