A mathematical model of solidification, that simulates the formation of channel segregates or freckles, is presented. The model simulates the entire solidification process, starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. A finite element model is used for the simulations. It uses a single system of equations to deal with the all-liquid region, the dendritic region, and the all-solid region. The dendritic region is treated as an anisotropic porous medium. The algorithm uses the bilinear isoparametric element, with a penalty function approximation and a Petrov-Galerkin formulation. The major task was to develop the solidification model. In addition, other tasks that were performed in conjunction with the modeling of dendritic solidification are briefly described. Poirier, David R. and Heinrich, J. C. Unspecified Center...