Peridynamics (PD), a recently developed theory of solid mechanics, which employs a non-local model of force interaction and makes use of integral formulation rather than the spatial partial differential equations used in the classical continuum mechanics theory, has shown effectiveness and promise in solving discontinuous problems at both macro and micro scales. In this paper, the peridynamics theory is used to analyze damage and progressive failure of concrete structures. A non-local peridynamic model for a rectangular concrete plate is developed, and a central pairwise force function is introduced to describe the interior interactions between particles within some definite distance. Damage initiation, evolution and crack propagation in the concrete model subject to in-plane uni-axial tension, in-plane uni-axial compression and out-of-plane impact load are investigated respectively. The numerical results show that discontinuities appear and grow spontaneously as part of the solution to the peridynamic equations of motion, and no special failure criteria or re-meshing techniques are required, which proves the potential of peridynamic modeling as a promising technique for analyzing the progressive failure of concrete materials and structures. Peridynamics (PD), a recently developed theory of solid mechanics, which employs a non-local model of force interaction and makes use of integral formulation rather than the spatial partial differential equations used in the classical continuum mechanics theory, has shown effectiveness and promise in solving discontinuous problems at both macro and micro scales. In this paper, the peridynamics theory is used to analyze damage and progressive failure of concrete structures. A non-local peridynamic model for a rectangular concrete plate is developed, and a central pairwise force function is Damage to, evolution and crack propagation in the concrete model subject to in-plane uni-axial tension, in-plane uni-axial compression and out-of-plane impact load are The numerical results show that discontinuities appear and grow spontaneously as part of the solution t o the peridynamic equations of motion, and no-special failure criteria or re-meshing techniques are required, which proves the potential of peridynamic modeling as a promising technique for analyzing the progressive failure of concrete materials and structures.