Membranes are thin extensible sheets that resist deformations due to stretching. In this talk we look at what happens when we apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. We also study the instability of a membrane to out-of-plane deflections by solving a nonlinear eigenvalue problem iteratively with large ensembles of initial guesses. Finally, we consider a simple physical setup: a membrane held by tethers with hinged ends and an infinite membrane model mounted on a periodic array of Hookean springs. Speaker(s): Christiana Mavroyiakoumou (University of Michigan)