Analcime under pressure undergoes a phase transition at ∼1.0 GPa from a cubic () form to a low-symmetry triclinic () form. We use geometric simulation to relate the pressure behavior of analcime to a recently discovered property of zeolite frameworks, the "flexibility window", defined as the range of densities over which the tetrahedral units in the framework can in principle be made geometrically ideal. Our results show that the range of stability of the cubic phase in analcime is defined by the flexibility window of the cubic framework. Analcime at low density can undergo tetragonal distortion while remaining within the flexibility window, consistent with experimental reports of non-cubic symmetries. On compression to higher densities, the capacity for tetragonal distortion is greatly reduced, accounting for the dramatic reduction in symmetry at the pressure-induced phase transition.