  We consider the formulation of the gravity theory first suggested by Regge
and Teitelboim where the space-time is a four-dimensional surface in a flat
ten-dimensional space. We investigate a canonical formalism for this theory
following the approach suggested by Regge and Teitelboim. Under constructing
the canonical formalism we impose additional constraints agreed with the
equations of motion. We obtain the exact form of the first-class constraint
algebra. We show that this algebra contains four constraints which form a
subalgebra (the ideal), and if these constraints are fulfilled, the algebra
becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of
Einstein's gravity. The reasons for the existence of additional first-class
constraints in the canonical formalism are discussed.
