A method and device provides for limiting fluid movement through a rent in a membranous tissue by forming a biocompatible and biodegradable barrier at the site of the rent. The barrier is formed by inserting into the rent a plug that includes connected water-swellable parts, so that within a short time following placement of the plug at the site the swellable parts expand in situ to form the barrier and occlude the rent. As fluids near the site are taken up by the swellable material, the material expands rapidly to fill the rent, engaging the marginal surfaces of the membrane near the edges of rent and forming a secure barrier at the site. All the materials of the plug are biocompatible and, over a period of time that allows for healing of the rent, all the components of the barrier are completely degraded without leaving any residual material at the site.