The macroscopic finite strain compressive behaviour of CNT/epoxy nanocomposites at quasi-static and high strain-rates was predicted and compared using 2D and 3D RVE approaches, a nonlinear and rate-dependent model for the epoxy matrix and nonlinear numerical homogenisation. Effects of CNT orientation, CNT volume fraction, CNT aspect ratio on the nanocomposite response were predicted and analysed, to compare 2D and 3D modelling approaches and obtain an insight into the nonlinear finite compressive behaviour of CNT/epoxy systems. It was found that the nanocomposite nonlinear compressive stress–strain response cannot be accurately captured by 2D RVEs (assuming the plane strain condition), when compared to 3D RVEs, primarily because of the stress transfer effect and the interparticle interaction accurately captured only in 3D. In general, 3D models predicted that the increasing CNT aspect ratio, CNT volume fraction and CNT alignment enhance the nonlinear finite strain compressive response by increasing the yield peak true stress and changing the post-yield deformation behaviour from softening to hardening. Also, the CNT alignment was identified as the major factor for enhancing the nonlinear stress–strain response at both quasi-static and impact rates of strain.