Impurity trapping generally occurs at the crystal surface during crystallization even if the solid-liquid phase equilibrium forms a simple eutectic type. However, the impurity profile inside crystal can not be predicted without measurement, because there is no theory to predict the impurity concentration of the crystal at the crystal surface during crystallization. In the present study, a new theory of solute/impurity distribution (segregation) at the crystal surface is proposed, and is applied to predict theoretically the impurity profile in the crystals grown from melt and solution. In order to predict the impurity trapping at the crystal surface, we have to predict exactly the profiles of impurity concentration and temperature in melt or solution near the crystal surface. Direct numerical calculations are conducted in order to solve the governing equations of heat, mass and momentum transports and to predict the impurity profile inside the crystal. The predictions were compared with the experiments for melt crystallization and suspension crystallization. An adaptive function was proposed to obtain the empirical relation from measurements. We will discuss on the impurity concentration in the crystal, crystal growth rate and physical properties at the crystal surface during crystallization.