An inverted container of water drains with a periodic glugging process where bubbles of air enter through the bottom hole, thus replacing the exiting water. If the container is soft, its walls can flex with each glug. We examine the effect of container elasticity on the drainage process. Experiments are conducted to measure the drainage rate and the glug period as water drains out of a container through a bottom hole. The container compliance is varied by varying the diameter of a soft rubber membrane comprising the lid of the container. Increasing container compliance (i.e., making the container softer) is found to increase the drainage velocity, increase the glugging period, and increase the volume of each glug. Previously, Clanet and Searby (2004) modeled the glugging process as a spring-and-mass oscillator where the compressibility of air in the headspace acts as the spring. We adapt this model so that the membrane elasticity acts in series with the air compressibility. This adapted model qualitatively agrees with the observations but underpredicts the observed effect on the glug period.