Abstract
<jats:p>The problem of longitudinal shear of an elastic layer fixed along its entire lower face and outside a certain strip of its upper face is considered. A rigid punch of finite width is applied to the free surface of the upper face. This punch does not cover the entire free surface and is subjected to a tangential load, creating the conditions for longitudinal shear. The solution is reduced to solving a system of singular integral equations on finite and semi-infinite intervals. The problem is solved using the mechanical quadrature method, which allows for a detailed numerical analysis of the dependence of contact stress distribution, stress concentration coefficients at the ends, and rigid punch displacement on the layer thickness and the width of the stress-free portion of the layer's upper face. The results are presented as graphs.</jats:p>