A two-dimensional model for extensional motion of a pre-stressed incompressible elastic layer near its cut-off frequencies is derived. Leading-order solutions for displacement and pressure are obtained in terms of the long wave amplitude by direct asymptotic integration. A governing equation, together with corrections for displacement 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.