Abstract: In many sectors and state administration agencies there is a great need in the software designed for specialized calculations like a popular MATLAB system combined with the Simulink graphical programming environment, but dealing with a particular database and task descriptions and not requiring any special payment. The main disadvantage of the MATLAB+Simulink package (apart from its price) is that the Simulink library of graphical primitives is in fact limited by popular and typical engineering calculating tasks. The author of the article emphasizes the need to develop the kind of programming environment which would be based on the freely distributed software. The programming environment described by the author supports on the 'client-server' concept and bases on the Java platform and web-technologies. The client uses the visual graphics editor implemented as a browser application. The server transmits data (task configuration) to the Octave calcuation package and vice versa, calculation results are transmitted to the browser. Data is transmitted online as the JSON line. The author creates the original programming architecture for specialized mathematical calcuation systems based on the freely distributed software. Taking into account the subsystem that stores the task configuration (and needs to be developed further), this architecture becomes the basis for creating specialized systems of the decision making processes in many spheres. The architecture provides a wide range of opportunities for further development.