In this work an analytical solution is used to explain the mechanism of dissolved sulfur influence on the transition from graphite to cementite eutectic in cast iron. It is found that this transition can be related to (1) the nucleation potential of graphite (characterized by nucleation coefficients, Ns and b (2) the growth rate coefficient of graphite eutectic cell, (3) the temperature range, Tsc = Ts - Tc (where Ts and Tc is the equilibrium temperature of the graphite eutectic and the formation temperature of the cementite eutectic respectively) and (4) the liquid volume fraction, fl after solidification of the pre-eutectic austenite. It has been shown that the main impact of dissolved sulfur on the transition from graphite to cementite eutectic consists in reducing the growth rate of graphite eutectic cell. Analytical equations were presented to describe the absolute chilling tendency, CT, and the chill, w of cast iron. Finally, it has been shown that as dissolved sulfur content in cast iron increases, the eutectic cell count, N, the maximum degree of undercooling at the onset of graphite eutectic solidification, ∆Tm, and the chilling tendency index, CT and chill, w increase as well.