Continuous rotary extrusion is mostly used for making sections of aluminium and copper alloys. This investigation expands the use of the technology by adding commercially pure titanium as a new workpiece material. The motivation was to improve mechanical properties of the extruded product through grain refinement. This paper gives the results of numerical modelling of the process performed with DEFORM software. Strain, strain rate and stress distributions within the workpiece during processing and the likelihood of defects in the product were determined. An analysis of the material characteristics of the workpiece is presented. The post-process ultimate strength was 580 MPa, whereas the initial elongation value remained without changes. The grain size upon processing was between 500 and 1000 nm. The resultant texture was basal in nature.