The initial kinking of a thin fracture process zone near the crack tip under plane strain is studied using the Wiener-Hopf method. The crack is located at the interface between dissimilar elastic media. The fracture process zone is modeled by a straight line of normal displacement discontinuity emerging from the crack tip at an angle to the interface. The angle between the process zone and the interface is determined from the condition of strain energy maximum in the process zone. The dependences of the length and angle of the process zone on the external load and other parameters îf the problem are studied. The results are compared with theoretical and experimental data obtained by other researchers Keywords: initial crack kinking, interface crack, thin process zone, Wiener-Hopf method Introduction. Studies of the failure mechanism for solids of different physical nature such as composites [2, 5], nanocomposites [18] reinforced ceramics and concrete [11,29], welded and adhesive joints [5] motivate theoretical developments on fracture mechanics based on new nonclassical models that take more complete (than in the classical models) account of the features of fracture process zones at crack tips. This issue is especially important in studying interface cracks between dissimilar media.It follows from [5,10,32,33] that if based on the classical approach (where a crack is regarded as an interface cut with no fracture process zone), a theoretical study of the stress and displacement fields at the edge of a cut-like crack leads to physically incorrect conclusions because the stresses and displacements at the edges of such a crack exhibit oscillatory behavior, which may result in overlapping of the crack faces. To avoid it, new approaches were developed in [3,4,12,13,15]. One approach is based on the studies [12,13,15], where the oscillations of the stresses and displacements are eliminated by introducing contact zones at crack tips. However, it was shown in [15,30] that the contact zone appears extremely small (subatomic) under pure tension, making the methods of continuum mechanics fail. Thus, eliminating one physical incorrectness with the help of the contact model, researchers in some cases arrive at another paradoxical result which raises doubts about this model. In [30], it is recommended to apply this model to pure shear only.The second approach is based on the Barenblatt and Leonov-Panasyuk-Dugdale models and their modifications and various models describing cohesive zones in polymers [2,17,19,21], ceramics [11], concrete [29], composites [2, 11, 19-22, 27, 28].When this approach is applied to cracks at the interface between dissimilar media in [3,4,11,14,17,31], the crack faces do not overlap and the fracture process zone under tensile forces is not extremely small, unlike the contact model.In studying the behavior of cracks at the interface between dissimilar materials (polymer-metal, polymer-composite) in [36], it was experimentally established that if the crack growth rate is low, the crack propagates in the ...