We study, within the Nambu-Goto approximation, the stability of massive string junctions under the influence of the tensions of three strings joining together in a Y-type configuration. The relative angle β between the strings at the junction is in general time dependent and its evolution can lead to zipping or unzipping of the three-string configuration. We find that these configurations are stable under deformations of the tension balance condition at the junction. The angle β relaxes at its equilibrium value and the junction grows relativistically. We then discuss other potential “unzipping agents” including monopole/string forces for long strings and curvature for loops, and we investigate specific solutions exhibiting decelerated zipping and unzipping of the Y junction. These results provide motivation for incorporating the effects of realistic string interactions in network evolution models with string junctions.