A new probabilistic model describing temporally random damage accumulation of tunnel concrete linings is proposed, in which independent two compound Poisson processes are used for (i) accumulation of daily small damages and (ii) accumulation of large damages due to severe frost damages, earth-quakes or other unusual phenomena. The model is based upon a random differential equation of Itô type driven by the two compound Poisson processes, whose solution and statistical moments are analytically derived. It is clarified that the proposed model can reproduce damage accumulation processes whose statistical tendency shows good agreement with actual damage data.