We demonstrate how to prepare extraordinarily deformable, gas-filled, spherical capsules from non-modified cellulose. These capsules have a low nominal density, ranging from 7.6 to 14.2 kg/m$^3$, and can be deformed elastically to 70% deformation at 50% relative humidity. No compressive strain-at-break could be detected for the se dry cellulose capsules, since they did not rupture even when compressed into a disc with pockets of highly compressed air. A quantitative constitutive model for the large deformation compression of these capsules is derived, including their high-frequency mechanical response and their low-frequency force relaxation, where the latter is governed by the gas barrier properties of the dry capsule. Mechanical testing corroborated these models with good accuracy. Force relaxation measurements at a constant compression rendered an estimate for the gas permeability of air through the capsule wall, calculated to 0.4 mLμm/m$^2$ days kPa at 50% relative humidity. These properties taken together open up a large application area for the capsules, and they could most likely be used for applications in compressible lightweight materials and also constitute excellent model materials for adsorption and adhesion studies.