It is studied a piecewise-homogeneous elastic plane which consists of two elastic half-planes. A system of thin rigid straight inclusions is located between the half-planes. One inclusion is disjoined from the plane and contacts it as a smooth rigid stamp. All other inclusions are perfectly joined the plane. It is considered the plane strain-stress state which is formed by stresses given at infinity. The problem is reduced to a combination of the Riemann-Hilbert matrix boundary value problem for analytic functions and the Hilbert-Dirichlet matrix boundary value problem. The combined boundary value problem is solved in an explicit form by reduction to two Riemann-Hilbert matrix boundary value problems on a two-sheeted Riemann surface. The complex potentials of the composite elastic plane and the stress intensity factors near the end-points of inclusions are found in an explicit form. The numerical examples are given.