The high speed spinning process of poly(ethylene terephthalate) was analyzed by 1-dimensional and 2-dimensional numerical simulations. The radius and the surface temperature of the fiber along the spin-line were calculated from the 1-dimensional numerical simulation. With the boundary conditions determined from the above, the temperature and the structure formation across the fiber radius were investigated from the 2-dimensional finite element method(FEM). To predict the neck-like deformation of the diameter profiles, the crystallization effect was included in the elongational viscosity term. The drastic increase in elongational viscosity with the crystallization of fiber brought about the neck-like deformation of the diameter profile and the concentration of the stress to the amorphous regions strengthened it. The effects of the process conditions on the formation of the fiber structure were investigated from the numerical simulations. The variations of the quench air velocities did not affect significantly in the on-line profiles of the fiber diameter, temperature, and structure. However, the variations of take-up velocities affected significantly on the on-line profiles of them and the structure of spun fibers. Mass flow rate played an important role in the determination of fiber radius and temperature profiles, but its effect on the final crystallinity of spun fiber was very small.