The work is devoted to the study of canonical formalism for one of the General Relativity modifications, the embedding theory. It is known that the embedding theory can be rewritten as General Relativity with an additional contribution of matter, which is called the embedding matter. The canonical description of such embedding theory is interesting for a better understanding of the embedding matter properties point of view. In this paper, we calculate all primary and secondary constraints, obtain the formulation of the Hamiltonian as a linear combination of constraints, and discuss the classification of the resulting constraints into constraints of the first and second classes. We solve some of the constraints, then the results for the considered embedding theory formulation in the form of GR with additional matter are compared with the already known results for the pure embedding theory.