A model for calculation of the compression resistance of a random assembly of carbon nanotubes (CNTs) is proposed. The model is based on the theory of geometry and compression of fibrous materials with randomly oriented fibres. It accounts for the orientation distribution and volume fraction of CNTs in the assembly, the bending rigidity of a CNT and its decrease after onset of buckling and for friction and slippage between CNTs. The model also allows for calculation the number of contacts between CNTs in the assembly and of the percolation threshold. The predicted compression resistance is compared with experimental data on compression of "buckydisks" made of CNTs. (C) 2011 Elsevier Ltd. All rights reserved.