A general dynamical model for disaster spreading is established in this paper, aiming at some common characteristics of key lifeline systems such as power supply network, water supply network, gas supply network, traffic network and communications network, etc. This model considers self-healing function, disaster spreading mechanism and internal stochastic noise of nodes. And the effects of three key parameters,namely the self-healing factor, duration delay factor and noise intensity, on recovery rate and number of damaged nodes for three different network topologies, i.e. Erdos-Renyi network, scale-free network and small world network are investigated. Simulation results are consistent with the characteristics of these true lifeline systems, showing that the presented model can effectively model disaster evolving dynamics for lifeline systems.