The paper proposes an original approach to solving the problem of ineffective processing of qualitative constraints of a subject domain using the constraint programming technique. The approach is based on the use of specialized matrix-like structures providing a “compressed” representation of constraints over finite domains, as well as on the use of the authors' inference techniques on these structures. In comparison with the prototypes using the typical representation of multi-place relations in the form of a table, the techniques make it possible to more efficiently reduce the search space. The paper presents practical aspects of implementation of user-developed types of constraints and corresponding algorithms-propagators, with the help of constraint programming libraries. The algorithms performance has been assessed by means of the above matrix structures to clearly demonstrate the advantages of representation and processing of qualitative constraints of a subject domain.