A spalling rate model is established to estimate the damage of concretes subject to the combined action of leaching and external sulfate attack (ESA). Two sub-models are developed to consider the different damage patterns. The profiles of sulfate and hydroxide ions are obtained from the solution of a dual moving boundary problem (MBP). The supersaturation of ettringite crystal is evaluated from these profiles, the effective stress is calculated through poromechanics for pore crystallization, and the spalling depth is determined using the fracture criterion. The experimental validation confirms the proportionality between the spalling depth and the square root of exposure time, and the models give conservative results but on the correct magnitude order for spalling depth. The parametric analysis shows the foremost impact of aluminate content and sulfate diffusivity on damage rate. The main assumptions in models lead to conservative predictions, but yet the model results are meaningful for engineering use.