  We consider two critical Rellich inequalities with singularities at both the
origin and the boundary in the higher order critical radial Sobolev spaces
$W_{0, {\rm rad}}^{k, p}$, where $1< p = \frac{N}{k}$. We give the explicit
values of the optimal constants of two critical Rellich inequalities for
radially symmetric functions in $W_{0, {\rm rad}}^{k, \frac{N}{k}}$.
Furthermore the (non-)attainability of the optimal constants are also
discussed.
