The concept of a computational web service that allows solving the problems of modeling of the microstructural properties during the solidification process is presented. The core of the service is projects (mathematical models) developed by researchers using one of the supported programming languages and corresponding solvers. The presented service allows scientists of the various level of immersion in the task to conduct cloud computing, to follow and analyze the computational results, save them on the server, and control access to the initial and final data. Using the developed service, it became possible to simulate the crystallization of binary compounds both regarding the flat front formulation of the problem and the extended phase transition (mushy) zone presence. The presented results make it possible to evaluate the microstructural dynamics of directional solidification and, in particular, the intensity of processes nearby the crystallization front.