We apply a model for thermotropic liquid crystalline polymers (TLCPs) that couples hydrodynamics, anisotropic rodlike microstructural dynamics, free surface effects, and thermodynamics to study fiber spinning of these materials. The model incorporates a Doi type theory for the nematodynamics, along with physical constants, empirical correlations for air drag and functional heat loss coefficient, and rheological relations that are consistent with the melt processing of TLCPs. This new single-phase model (Forest et al., 1998) does not arbitrarily assume a rigid fiber of constant velocity below glass transition temperature of the TLCP, a feature that allows a multiparameter stability calculation of the critical draw ratio. For this study, fiber spinning steady states are computed in experimentally based physical regimes. We predict spun fiber performance properties (birefringence, modulus, and axial force), process sensitivity, and bounds on throughput (draw ratio) due to heat loss, air drag, the temperature variation between the melt and ambient, and the material properties of TLCPs.