Carbon nanotubes (CNTs) have very high mechanical properties and that is why they are used for making super strong and light yarns, ropes, fillers for composites, solid lubricants, etc. Mechanical properties of CNT bundles have been addressed in a number of experimental and theoretical studies. Development of efficient computational methods for solving this problem is an important step in design of new CNT based materials. In the present study, an atomistic chain model is used to analyse mechanical response of CNT crystal under plane strain conditions. The model takes into account tension and bending of CNT wall and the van der Waals interactions. Discrete character of the model allows description of large curvature of CNT wall and CNT fracture at very high pressure. Equilibrium structures of CNT crystal under biaxial, strain controlled loading are obtained and the potential energy of the structure is decomposed into the energy of valence bonds, valence angles and van der Waals interactions. It is shown that the main contribution to the potential energy comes from the energy of valence angles related to bending of CNT walls. The reported simulation results are in a good agreement with the existing literature. The chain model offered here can be efficiently applied to the analysis of mechanical properties of single-walled or multi-walled CNT bundles under plane strain conditions or, under straightforward modifications, to similar structures made of other 2D nanomaterials.