Elasto-capillarity, the interaction between elasticity and surface tension or surface energies, has been much studied in recent years. However, to date the focus has been almost exclusively on situations where the bending stiffness of an object resists deformation by the surface tension of a liquid. In this talk I will consider two situations in which it is instead the stretching stiffness of an elastic object that resists its deformation by surface tension. The first example involved the recent experiments demonstrating the wrinkling of floating elastic membranes [J. Huang et al., Science 317:650 (2007)]. I will show how membrane theory modified to account for the various surface energies involved explains some of the properties of the wrinkling pattern. The second example involves the delamination of thin elastic sheets from soft substrates and is motivated by methods used to manufacture flexible electronic devices.