The authors construct a numerical algorithm for the determination of stress field in an elastic plane with crack. Some unknown parts of the crack, which are in contact, must be determined as well. Zero traction on the open part of the crack, zero friction, negative normal traction and zero normal crack-opening displacement in the contact zone, and closure of the crack are described by integral equations and inequalities. The corresponding integral operators are constructed following the well-known Muskhelishvili method. The algorithm is based on a rapidly converging sequence of Fredholm integral equations of the second kind which treat the contact problem as a perturbation of a crack problem without contact. Four examples are solved numerically: circular arc-shaped crack in symmetric contact; circular arc-shaped crack in asymmetric contact; crack with wavy shape in contact; and circular arc-shaped crack with contact at crack tip. The results obtained for the last example are compared with known results in the existing literature.