The effect of hydrostatic pressure on structural and magnetic characteristics of the two-dimensional ferromagnetic K2CuF4 is studied using a pair interaction model for the crystal energy. Multi-body Jahn-Teller (JT) contributions to the energy are also taken into account. It is predicted that application of hydrostatic pressure induces a first order structural transition which gives rise to antiferromagnetic ordering of the copper spins within the c-plane.