Two-dimensional finite 'crack' elements for Simulation of propagating cracks are developed using the moving least-square (MLS) approximation. The mapping from the parental domain to the physical element domain is implicitly obtained from MLS approximation, with the shape functions and their derivatives calculated and saved only at the numerical integration points. The MLS-based variable-node elements are extended to Construct the crack elements, which allow the discontinuity of crack faces and the crack-tip singularity. The accuracy of the crack elements is checked by calculating the stress intensity factor under mode I loading. The crack elements turn out to be very efficient and accurate for simulating crack propagations, only with the minimal amount of element adjustment and node addition as the crack tip moves. Numerical results and comparison to the results from other works demonstrate the effectiveness and accuracy of the present scheme for the crack elements. Copyright (c) 2005 John Wiley & Sons, Ltd.