Cellulose-based materials draw their good mechanical properties from the cellu-lose crystal. Improved understanding of crystal properties could lead to a wider range of applications for cellulose-based materials, Cellulose crystals show high axial Youngs modulus. Cellulose can attain several allomorphic forms which show unique structural arrangements in terms of both intra-molecular and inter-molecular bonding, as well as unit cell parameters and chain packing. Although several studies have confirmed that mechanical tensile properties of cellulose differ between different allomorphic forms, few reports have investigated the deformation mechanisms explaining the differences.In the first part of this thesis, the tensile elastic Youngs modulus of cellulose allo-morphs Iβ, II and III I were calculated under uniform conditions using Molecular Dynamics simulation techniques. As expected, a difference in modulus valuesc ould be observed, and the cooperative nature of energy contributions to crys-tal modulus is apparent. The allomorphs also show large differences in terms of how contributions to elastic energy are distributed between covalent bonds,angles, dihedrals, electrostatic forces, dispersion and steric forces.In the second part of this thesis, the cellulose Iβ and II allomorphs were sub-jected to a more detailed structural study. The purpose was to clarify how the deformation of the central glucosidic linkage between the monomer units depends on the hydrogen-bonding structures. This was carried out by studying simulated vibrational spectra and local deformations in the crystals.The results presented in this thesis confirm the differences in the tensile elastic properties of these cellulose allomorphs. These differences can in part be explained by the different intra-molecular hydrogen bonding patterns between allomorphs. Deformation mechanisms are discussed. The results are in supportof the so called ”leverage effect” proposed in the literature. The present analysis shows significant differences in details of deformation mechanisms compared with previous simpler analyses.