In this study compressive strength of carbon nanotube (CNT)/cement composite is computed by analytical method. For this purpose representative elementary volume (REV) as an indicator element of composite is chosen and analyzed by elasticity relationships and Von mises' criterion applied to it. It is assumed that carbon nanotubes are distributed uniformly in the cement and there is perfect bonding in the interface of cement and nanotube. At first for simplicity of computations, carbon nanotubes ( CNTs) are assumed to have unidirectional orientation in the cement matrix. In following, the relations are generalized to consider random distribution of nanotubes in cement, and a new factor suggested for random orientation of fibers in the CNT/cement composite. The results of analytical method are compared with experimental results.