You might try a displacement boundary/condition on the proposed surface in the model - probably something very small.
If you expect much deflection then this could easily turn into a non-linear problem. You should probably also consider the friction coefficient of the glass to your 'cork' especially if you are expecting internal pressure.
The reason cork is used as bottle stopper is because it has a very unique property - the Poisson's ratio is nearly zero. That is to say it doesn't expand (much) when you load it in compression to get it in the bottle neck.