Using the analogy with the problem of ionization and
excitation of atoms at the propagation of relativistic charged particles through
matter, the process of Coulomb dissociation of weakly bound relativistic nuclei
and hypernuclei is theoretically investigated in the framework of the
two-cluster deuteron-like model. On the basis of the general formula for the
total cross-section of excitation and dissociation of a relativistic nucleus in
the Coulomb field, explicit analytical expressions for the total cross-section
of Coulomb disintegration of weakly bound systems are derived, taking into
account also the additional correction terms connected with the finite size of
the target nucleus. Numerical estimates for the Coulomb dissociation of
relativistic hypernuclei $^{3}H_{\Lambda}$ and $^{6}He_{\Lambda}$ are
performed, and it is demonstrated that for these cases ( especially --
for $^{6}He_{\Lambda}$ ) the corrections due to the finite size of the
target prove to be rather essential.

It is shown that in the limit of
very small binding energies $\varepsilon_{{\rm bin}}$
the cross-section of Coulomb dissociation increases
inversely proportionally to $\varepsilon_{{\rm bin}}$,
and -- due to such a sharp dependence upon the binding
energy -- the experimental measurement of this
cross-section in the case of weakly bound relativistic nuclei
and hypernuclei allows one to determine the values of binding
energy for these systems.