Numerical algorithm to simulate 2-D smooth crack growth is presented. The stepwise method based on local criteria of propagation is used. Two crack propagation criteria are employed. At the first stage of popagation, the maximum tensile stress criterion is used to take into account the abrupt change in tangent direction. At subsequent stages, the assumption that the stress intensity factor (SIK) K2=0 at the current crack tip is exploited. The analytical formulae for calculating SIF's are given. The displacement discontinuities (DD) involved in these formulae are found from the numerical solution of a complex hypersingular integral equation (CHSIE) for a piecewise homogeneous plane with a curvilinear cracks. The new mechanism of smooth approximation of the crack path by circular arcs at each propagation stage is suggested. Numerical results are given. They confirm the efficiency of the algorithm suggested.