A new damage-healing model for self-healing cementitious materials is described. The model is formulated using results from a discrete ligament model and guided by the findings of a linked experimental study. Healing is simulated using the interaction of curing fronts propagating from opposing crack faces within a body of healing-agent. This approach accounts for the dependency of the healing response on the crack opening displacement (COD) and its rate. The new damage-healing cohesive-zone model is applied to an element with an embedded strong-discontinuity within a coupled finite-element code, which simulates healing-agent transport and mechanical behaviour. The model is validated using data from tests with different CODs and COD rates. The validations show that the coupled model represents the mechanical and flow behaviour of an autonomic self-healing system with good accuracy for a range of cracking configurations and load paths.