Several problems involving a one-dimensional continuum with a free boundary are examined. These are: peeling of adhesive tape from a surface; sliding of a segment of a stretches string pressed against a rough plane under the influence of transverse loads; lengthwise splitting of a beam is considered; stability of a beam split further by a machine which pulls the ends (two halves of one end) apart quasistatically; and peeling of an elastica from a plane surface to which it adheres.