The drawing process for the fabrication of a hollow optical fiber involves the flow of glass, which is largely heated by thermal radiation, in an inert gas environment. It is critical to maintain the central core, which can collapse if the thermal conditions are not properly imposed and controlled. This paper presents the analysis and simulation of this complicated process. A numerical model is developed, validated, and applied to simulate the hollow optical fiber drawing process under a wide range of boundary conditions, particularly draw speed, tension, and temperature. A feasible domain of the drawing process is identified to give the range of the drawing parameters for which the geometry of the fiber is maintained and collapse of the core and viscous rupture of the fiber are avoided. The effects of drawing temperature and feeding speed, which are crucial factors in determining the geometry and quality of the fiber, are investigated in detail. A multi-variable unconstrained optimal design problem is posed and considered in terms of the feasible domain. An appropriate objective function, comprised of the maximum velocity lag, thermally induced defect concentration and draw tension, is proposed to quantify the quality of the hollow fiber. The univariate search method is then applied to obtain the optimal drawing temperature and feeding speed. This study provides a basis for the optimization of hollow fiber drawing process and indicates that a substantial improvement in fiber quality can be achieved.