  The problem of constructing an exact solution of singular
integro-differential equations related to problems of adhesive interaction
between elastic thin semi-infinite homogeneous patch and elastic plate is
investigated. For the patch loaded with horizontal forces the usual model of
the uniaxial stress state is valid. Using the methods of the theory of analytic
functions and integral transformation the singular integro-differential
equation is reduced to the Riemann boundary value problem of the theory of
analytic functions. The exact solution of this problem and asymptotic estimates
of tangential contact stresses are obtained.
