Summary: A non-local isotropic damage model is proposed which can be used to predict the behaviour of rock-like materials up to failure. Two isotropic damage variables account for the progressive degradation of mechanical properties under stress states of prevailing tension and compression, and two internal lengths (one for tension and the other for compression) are introduced as localization limiters. A linear bifurcation analysis highlights the regularization properties of the non-local model. We also present an iterative scheme for numerical solution of the finite-step problem. The scheme consists of a linear global predictor, an averaging phase, and a nonlinear local corrector. Some examples of tension and splitting tests show the effectiveness of the proposed model.