SUMMARY Numerical simulation of large deformation and failure problems present a series of difficulties when solved using mesh based methods. Meshless methods present an interesting alternative that has been explored in the past years by researchers. Here we propose a Runge–Kutta Taylor SPH model based on formulating the dynamic problem as a set of first‐order PDEs. Two sets of nodes are used for time steps n and n + 1 ∕ 2, resulting on avoiding the classical tensile instability of some other SPH formulations. To improve the accuracy and stability of the algorithm, the Taylor expansion in time of the advective terms is combined with a Runge–Kutta integration of the sources. Finally, as boundaries change during the process, a free surface detection algorithm is introduced. Copyright © 2012 John Wiley & Sons, Ltd.