  In this paper, we consider the problem of quantization of classical St\"ackel
systems and the problem of separability of related quantum Hamiltonians. First,
using the concept of St\"ackel transform, all considered systems are expressed
by flat coordinates of related Euclidean configuration space. Then, the
so-called flat minimal quantization procedure is applied in order to construct
an appropriate Hermitian operator in the respective Hilbert space. Finally, we
distinguish a class of St\"ackel systems which remains separable after any of
admissible flat minimal quantizations.
