The coagulation process of PAN (poly(acrylonitrile)) wet-spinning was modeled and simulated based on the numerical analysis of the coagulation of a viscous polymer solution by diffusional interchange with a bath. Experiments were performed with gelled solutions of PAN in nitric acid to determine the diffusion rate of solvent and nonsolvent (water) during the coagulation. The experimental data were analyzed by using equations of diffusion coefficient which are a function of the solvent concentrations of the coagulation bath and the filament. The concentration profile of solvent in moving filament was predicted by solving the diffusion model equation numerically. A simplex method was used in the computation of the parameters of the diffusion equations to minimize the difference between the numerical results and experimental data.