Milling cutters with fir-slot (fir tree cutters) are widely used in the high speed machining of blade-root and rotor-groove. The complicated structures and multitudinous specification sizes make it difficult to achieve an accurate three-dimensional (3-D) parameterised modelling of the cutter. In this paper, the conical helix and radial cross-sectional curves are expressed mathematically based on geometric curve and surface theory. The radial geometric angles are calculated from the normal angles based on the analysis of the relationship between radial section and normal section. Finally, rapid generation of the 3-D model of fir tree cutters and information interaction with computer aided engineering (CAE) software are realised. The results show that the established mathematical model can efficiently express the fir tree cutters, which improves the efficiency and accuracy of cutter design. [Received 22 April 2016; Accepted 1 December 2016]