The paper concerns the plane-strain problem of a rigid cylinder pressed between two identical elastic layers supported by rigid bases along which they may slide without friction. The essential difficulty of the problem is that there are three contact zones, one between the cylinder and the layers, and two, symmetrically placed, between the layers; the extent of these regions has first to be found. Alblas has given an iterative solution to the problem which reduces to a closed-form solution when the layers are half spaces. The purpose of the paper is to show that there is an elegant approximate solution of the half-space problem which is well suited to computation and which converges to the closed-form solution. The solution depends on some remarkable results obtained by extending the Chebyshev polynomials to the whole of the real line. The paper also provides a single-step approximate solution of the two-layer problem.

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