Samples of oxygen-free high conductivity (OFHC) coarse-grained (CG) and ultrafine-grained (UFG) copper were micro-extruded to an equivalent strain of 2.8 in one pass at room temperature. Samples of the OFHC copper were annealed at 650 C for 2 h to produce CG copper. Some samples were subsequently processed by equal channel angular pressing of eight passes, route Bc, at room temperature to produce the UFG material. Crystallographic texture and misorientation distributions were obtained locally from EBSD mappings at different radial positions after micro-extrusion. To model the strain path during micro-extrusion, the analytic flow line model of Altan et al. [J Mater. Process. Tech. 33 (1992) p.263] was used and also validated by finite element calculations. Modelling was carried out using the viscoplastic self-consistent (VPSC) model and a recently developed grain refinement model. The results showed large texture variations along the cross-section of the extruded sample for both UFG and CG copper. These cyclic drawing textures in UFG copper were simulated in good agreement with experiments using the presented modelling framework.