The high-pressure structures of AlPO4-5 (Al12P12O48•9.9H2O) and SSZ-24 (Si24O48) with the same AFI framework topology were studied using synchrotron X-ray powder diffraction and a pore-penetrating (at a mixture of 16:3:1 by volume of methanol:ethanol:water) pressure medium. An analysis of the diffraction profiles of the AlPO4-5 reveals that the a-axis length expands initially before it starts to contract, whereas the c-axis contracts steadily throughout the pressure range up to 5 GPa. As a result, the unit cell volume at 0.7(1) GPa appears larger by 3σ than that at ambient conditions, and the bulk modulus after this initial volume expansion is calculated to 50.5(7) GPa. In the SSZ-24, the unit cell contraction is monotonic with a steeper slope than that of AlPO4-5 leading to a smaller bulk modulus of 21.7(3) GPa. The reason for the two contrasting compression behaviors of the AFI frameworks is suspected to be related to the difference in the hydrophobicity of the framework and hence the water distribution in the channel. To evaluate the effect of the pressure medium, the experiment on SSZ-24 was repeated using a non-penetrating silicone oil pressure medium and laboratory X-ray powder diffraction. The bulk modulus of SSZ-24 was found to the same low value of 21.7(3) GPa demonstrating that the measured compressibility of SSZ-24 is inherent to the AFI framework type.