In this Letter, we report the unusual behavior of zeolites with LTA structure (a prototype of synthetic zeolite) under high external pressure. We found that these materials undergo pressure-induced amorphization. Interestingly, the pressure-induced amorphization is reversible for some of these materials. Apparently, the amorphization occurs via the weakening of the double four membered rings in zeolite lattice. We found that the structural memory of the glasses and the stability of the LTA zeolites depend strongly on the nature of the charge balancing cations present in the framework.