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This study presents a boundary value problem (BVP) formulated in terms of principal directions given on surfaces of curvilinear cracks in a plane.Tractions on crack surfaces are usually assigned in formulations of boundary value problems for plane cracks [1]. This does not meet difficulties for open cracks but for bodies subjected to compressive or shear loading crack surfaces may be in full or partial contact. The latter substantially complicates formulation of conventional BVPs due to a-priory unknown positions of contact zones.An alternative approach is suggested to deal with partly closed cracks; it assumes principle directions on cracks contours while stress magnitudes remain unknown. Such types of BVPs have been reported for simply connected domains bounded by closed contour [2-3] but not studied for open contours so far.General formulation for a system of curvilinear cracks is presented. The method of integral equations is adopted that investigates solvability and provides a basis for numerical analysis.It is shown that BVPs posed in terms of stress orientations has several linearly independent solutions, their number is determined by behavior of principal directions on the crack contours