Experimental deformation micromechanics of natural cellulose fibers using Raman spectroscopy and X-ray diffraction have been widely reported. However, little has been published on the direct measurements of the mechanical properties, and in particular the elastic modulus, of the highly crystalline material in the native state. Here we report on measurements of the elastic modulus of tunicate cellulose using a Raman spectroscopic technique. A dispersed sample of the material is deformed using a four-point bending test, and a shift in a characteristic Raman band (located at 1095 cm^-1) is used as an indication of the stress in the material. Relatively little intensity change of the Raman band located at 1095 cm^-1 is shown to occur for samples oriented parallel and perpendicular to the polarization direction of the laser, as compared to a highly oriented flax sample. This indicates that the tunicate sample is a two-dimensional in-plane random network of fibers. By use of this result, the Raman shift, and calibrations with strain from other materials, it is shown that the modulus of the material is very high, at about 143 GPa, and a lack of Raman band broadening is thought to be due to the fact that there is pure crystalline deformation occurring without the effect of crystalline/amorphous fractions. A strain sensitivity of the shift in the 1095-cm^-1 Raman peak for this specimen is shown to be −2.4 ± 0.2 cm^-1/%. A molecular mechanics approach, using computer simulation and an empirical force field, was used to predict the modulus of a highly oriented chain of the material, and this is found to be 145 GPa, which is in agreement with the experimental data. However, by use of a normal-mode analysis, it is found that a number of modes have positions close to the central positions of the experimental Raman band. One in particular is found to shift at a rate of 2.5 cm^-1/%, but due to the complex nature of the structure, it is not entirely conclusive that this band is representative of the experimental findings.