As the first step for a probabilistic LBB (Leak Before Break) evaluation, the random propagation of surface cracks of semielliptic type was investigated by considering the randomness of loading and material properties. First, by the use of a Markov approximation metod, the joint probability density function of surface length and depth of a surface crack was derived in a closed form, under the assumption that the shape of surface crack is always semi-elliptical and the well-known Paris' fatigue crack propagation law is applicable for its propagation in both surface and depth directions.Next, a failure criterion for the two-dimensional crack propagation was constructed. Based upon this criterion, the so-called residual life distribution was theoretically derived by the use of the crack length density function. Finally, a more detailed form of the residual life distribution function under stationary random loading was studied under the condition that the material property was not random, and its qualitative behavior was clarified by numerical calculations.