Presented in this paper is a simple two-dimensional model to examine the effects of sub-surface irregularities on the strength of multi-year ice. The irregularities cause bending moments which can lead to surface tensile stresses. When these tensile stresses are sufficiently high for crack nucleation to occur, a very brittle fracture of the entire ice sheet will ensue. The fracture is brittle because, for the large grain sizes in the natural ice cover, the stress required for crack nucleation is greater than that necessary to propagate a crack. The theory has been examined with experimental laboratory tests on columnar ice. The importance and significance of the results are that old thick multi-year ice in winter conditions may be substantially weaker than expected, and thus it is the limited strength of the multi-year ice that may dominate design ice forces on arctic structures rather than a limited driving force.