In order to study the process of rectangular fiber melt spinning, experimental and theoretical investigations are conducted. Several different values of such process variables as die dimension, flow rate, take-up speed, quench air speed and temperature, and die temperature are chosen for manufacturing poly(ethylene terephthalate) fibers. Both 1- and 2-dimensional formulations are employed under the Newtonian fluid assumption. Two separate mathematical schemes are then combined via the Picard iteration to provide a convenient tool estimating the process with all variables taken into account and with as little computational effort as possible. From this experiment, it is found that the extrudate exhibits negative swelling in the fiber width direction, which results from the negative second normal stress direction in shear flow inside the die. Fiber cross-section takes elliptical shape at the point of maximum thickness swell and then gets flat as it approaches that take-up point. As to numerical simulation, all the quantities such as fiber dimension, velocity, temperature and tension except variables related to cross-sectional are are relatively well described by this simple theory. Neglect of material elasticity and over-simplification of temperature variation along fiber cross-section are main causes for the deviation of calculated values from experimental data.