Phase field models have played an important role in shaping our understanding of a variety of micro structural phenomena in materials. Their attractive features include (a) their ability to capture instabilities in microstructures, and (b) their ability to handle topological transitions { such as splitting or coalescence { gracefully. Therefore, we have chosen to use a phase field model in our study of instabilities in cylindrical pores in nanoporous membranes which eventually lead to their failure. Our study is motivated by recent studies on thermal stability of nanoporous membranes of alumina, titania and zirconia. The key feature in our model is its ability to incorporate surface discussion as the mechanism for mass transport. We first benchmark the model through a critical comparison of our results on early stages of surface evolution during Rayleigh instability and grain boundary grooving with those from linear theories of these phenomena. We have then used longer simulations (which go beyond early stages, and therefore, can incorporate non-lineare effects) to study instabilities in a hollow cylinder in three different systems: single crystal or amorphous solid (which fails through Rayleigh instability), a model sys-tem with parallel grain boundaries (which fails through grain boundary grooving), and a polycrystal (whose failure depends on a combination of grain growth and grooving). In all the cases, the surface energy is assumed to be isotropic, and the operative mechanism for mass transport is assumed to be surface discussion.