The present work considers two-dimensional non-linear wave propagation in an infinite, homogeneous micropolar elastic medium. The reductive perturbation method is directly applied to a Lagrangian whose Euler-Lagrange equations give the field equations for a geometrically non-linear micropolar elastic medium. It is shown that the behavior of non-linear waves in the long-wave approximation is governed by the two-coupled modified Kadomtsev-Petviashvili equations. Travelling wave solutions of the non-linear evolution equations are considered by means of a modified Hirota method. (C) 1998 Elsevier Science Ltd. All rights reserved.