As a first step for the probabilistic LBB assessment, random propagation of a semi-elliptical surface crack is investigated as a bivariate stochastic process. Based upon a few assumptions, the Fokker-Planck equation to describe a temporal variation of probability distribution of this bivariate process is first derived by the use of the Markov approximation method, and its analytical solution is obtained. Next, by constructing a failure criterion for the surface crack propagation, the so-called residual life distribution for the surface crack is derived. Further, the more concrete expression of the residual life distribution is calculated under the condition of stationary random loading but constant propagating resistance and its behavior is clarified through numerical calculations.