This paper presents the numerical simulation of free surface waves in a 2D domain which represents a wave tank, using a localized approach of the meshless radial basis function (RBF) method. Instead of global collocation, the local approach breaks down the problem domain into subdomains, leading to a sparse global system matrix which is particularly advantageous in tackling the time consuming simulation process. Mixed Eulerian-Lagrangian approach is adopted for free surface tracking and fourth order Adams-Bashforth-Moulton scheme (ABM4) is used for time stepping. Both linear and nonlinear Stokes waves are simulated and compared to analytical solutions. (C) 2011 Elsevier Ltd. All rights reserved.