This paper proposes a method to solve problems for interface tunnel defects in a piecewise-homogeneouselastic material that is under generalized plane strain and has no planes of elastic symmetry. The method is based on integral relations between the discontinuities and sums of the components of the displacement vector and stress tensor at the interface. Closed-form solutions are obtained for a system of interface tunnel inclusions with mixed contact conditions between the space and the inclusions. The dependences of the indices of singularity of the solutions on orthogonal coordinate transformation are established for different combinations of materials of monoclinic and orthorhombic systems. The effect of the antiplane component on the behavior of the solutions is revealed

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