A cell-based smoothed radial point interpolation method (CS-RPIM) is developed for fracture problems. The strain smoothing is performed over background triangular cells. The stiffness matrix is calculated based on the weakened weak formulation, using shape functions obtained by radial point interpolation method. A layer of five-node singular elements are used to simulate the singularity around the crack tip. Different schemes are devised in the five-node elements to perform the strain smoothing. Several examples are presented to validate the newly developed method. The results are found in excellent agreement with the exact (or reference) solutions. (C) 2011 Elsevier Ltd. All rights reserved.