The drawing process is important for basalt fibre production. Studies of the flow and heat transfer in the process can contribute to raising the quality/strength of basalt fibre & avoiding fibre breakage. A numerical model describing heat transfer & flow in the fibre drawing of basalt fibre was constructed. Numerical simulation was based on appropriate simplifications. The geometrical shape, temperature, velocity & viscosity distributions of the fibre were obtained by solving the continuity, momentum & energy equations using the finite differential method. The governing equations were discretised in a tridiagonal matrix form & were solved using the tridiagonal matrix algorithm & the alternative direction implicit solver. Results showed that the basalt fibre cone is tapered, the rate of change of radius decreasing with distance from nozzle.