Based on numerical simulation of the nonstationary process of directional solidification of a weak solution flat–front within locally the non–equilibrium phase–field model study of the process of redistribution of the impurity in the vicinity of the diffuse boundary between the liquid and solid phases. As a result of numerical modeling, profiles of the average impurity concentration near the interface are obtained. From the obtained profiles of the average concentration, the distribution of concentrations in the solid and liquid phases at different speeds of the front movement is determined using the phase field. The constructed graphs of the dependence of the distribution coefficient on the velocity are compared with the data for the hyperbolic model of continuous growth and previously performed calculations in the quasi–stationary approximation. The influence of the model parameters on the type of dependence of the distribution coefficient on the front velocity and on the distribution profile of the concentration inside the diffuse interface is studied.