The compressive responses of an interlayer of the dry sodium-montmorillonite (Na-MMT) swelling clay as well as the clay intercalated with organic fluids of a wide range of dielectric constants from 110 (formamide) to 20 (acetone) are quantitatively evaluated using steered molecular dynamics simulations. Representative dry clay and clay with fluid (clay-fluid) molecular models are constructed, and the stress-strain relationships upon compression of these models are studied using constant force steered molecular dynamics (SMD) simulations. Our results show that the polarity of the fluids and the amount of the fluid molecules in the clay interlayer play a significant role in the interlayer spacing, interlayer volume, interlayer strain, interlayer modulus, nonbonded interactions, and conformation of the fluid molecules upon externally applied stresses. The clay interlayer responses upon compression are essential for the development of multiscale modeling of swelling clays and prediction of the reliable compressive behavior, which are critical for the accurate analysis and economical design of the infrastructures in swelling clay areas and the densification of clays for ceramics manufacturing.