A new generalized Jacobi elliptic function method is used for constructing exact travelling wave solutions of non-linear partial differential equations in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new double periodic and multiple soliton solutions are obtained for the generalized (2 + 1)-dimensional Boussinesq equation. This method can be applied to many other equations. (C) 2003 Elsevier Ltd. All rights reserved.