A theory is presented for the dynamics of slender sheets of viscoplastic fluid. First a model suitable for relatively small curvature is presented and applied to the fall of a liquid bridge supported at its two ends. Second, order-one curvatures are considered, along with the sagging of a beam with a free end that is either emplaced or extruded horizontally. We then present a theory combining both limits of curvature, and consider the buckling of a nearly vertical column. Analogous models for a circular viscoplastic thread are also discussed. (C) 2012 Elsevier B.V. All rights reserved.