We present a translation and analysis of a cosmic model published by Einstein in 1931. The paper, which is not widely known, features a model of a universe that undergoes an expansion followed by a contraction, quite different to his static model of 1917 or the monotonic Einstein-de Sitter model of 1932. The paper offers many insights into the cosmology of Albert Einstein in the light of the first evidence for an expanding universe, and we discuss his views of issues such as the curvature of space, the cosmological constant, the singularity and the timespan of the expansion. We argue that retrospective descriptions of this model as cyclic or periodic are not historically or mathematically accurate. We find that calculations in the paper of the matter density and radius of the universe contain a numerical error, a finding that is supported by writing on a blackboard used by Einstein during a lecture at Oxford University in May 1931. Our article concludes with a general discussion of his philosophy of cosmology.