The refractive indices of RbAlSi3O8 and CsAlSi3O8 glasses in the range of pressures up to 6.0 GPa were measured using a polarisation-interference microscope and a diamond anvil apparatus. The changes in the relative density which characterise the compressibility of the glasses were estimated in the pressure range under investigation from the measured refractive indices within the framework of the theory of photoelasticity. Although the molar contents of Al2O3 and M2O are identical in the MAlSi3O8 glasses (M=Na, K, Rb, Cs), the isothermal initial bulk modulus (Kt,o) of these glasses decreases in the order Na+, K+, Rb+, and practically does not change when Rb+ is replaced by Cs+. This change in Kt,o indicates an increase in the degree of polymerisation of the structural network of the glasses containing Rb+ or Cs+. The increase in Kt for glasses in teh series of alkali metal cations can be explained by teh fact that the voids are occupied by cations K+, Rb+, Cs+, which have a larger orbital radius than Na+, and more strongly inhibit compression.