Abstract <p>We construct an exact solution to the boundary value problem of the theory of elasticity for a free infinite strip with a one-dimensional transverse stiffener whose length is equal to the strip width. An external load acts along the stiffener. Only an even-symmetric deformation is considered. First, we solve the inhomogeneous problem for a free strip and then, on its basis, the problem for a strip with a stiffener. The final solution is represented by series in Papkovich–Fadle eigenfunctions. This solution is compared with the solution for an unbounded elastic plane with an infinite one-dimensional stiffener and with its numerical elastic simulation in ZSoil, a certified finite element software.</p>