AbstractThe radial point interpolation method (RPIM), as an advanced discretization approach, is used to analyze concrete structures assuming a non-linear continuum damage model. The theoretical basis of the material, damage characteristics and the computational procedure are presented. The elastic model is extended with a non-local damage formulation for compressive stress state from the Helmholtz free energy function in relation to the damage energy release. The predictive ability of the non-local model will be compared with the local solution, which is inappropriate whenever strong strain softening is encountered. Due to the presence of damage, the Newton-Raphson non-linear algorithm is employed, creating a fictitious pseudo-time stepping scheme. The performance of the proposed model is verified with an experimental benchmark available in the literature.