An algorithm for solving the problem of slow propagation of mode I crack with partial closure is proposed. The algorithm is based on the cohesive zone model, iterative method for constructing elastic solutions, and the principle of elastic-viscoelastic correspondence, which allows us to obtain the time-dependent separation in the Boltzmann—Volterra form. As a criterion for crack propagation, the crack-tip-opening displacement fracture criterion is used with constant crack tip opening displacement and cohesive strength during the quasistatic crack growth. The algorithm is illustrated by the numerical example with tensile stress at infinity and the system of two point forces symmetric with respect to the crack line, which cause the contact of crack faces. During the crack propagation, the contact zone disappears, which is accompanied by the rapid transition to the dynamic stage of fraction.