Continuous casting process is numerically analyzed using the continuum model in a non-orthogonal coordinate system. Flow damping in the mush is modeled by combining the viscosity dependence on liquid fraction in dilute mush and the permeability dependence on liquid fraction in concentrated mush. The effect of turbulence is indirectly considered by effective diffusivity determined elsewhere by experiment. The main objective is to investigate the effects of casting parameters such as casting speed and tundish superheat on the distribution of surface temperature, shell thickness, metallurgical length and centerline segregation. Some of the computed results are compared with available experiments, and reasonable agreements are obtained.