Thin glow discharge polymer (GDP) shells are currently used as the targets for cryogenic direct drive laser fusion experiments. These shells need to be filled with nearly 1000 atm of D2 and cooled to cryogenic temperatures without failing due to buckling and bursting pressures they experience in this process. Therefore, the mechanical and permeation properties of these shells are of utmost importance in successful and rapid filling with D2. In this paper, we present an overview of buckle and burst pressures of several different types of GDP shells. These include those made using traditional GDP deposition parameters ("standard GDP") using a high deposition pressure and using modified parameters ("strong GDP") of low deposition pressure that leads to more robust shells.