  We develop a scheme to construct the Hamiltonians of the lambda, vee and
cascade type of three-level configurations using the generators of SU(3) group.
It turns out that this approach provides a well defined selection rule to give
different Hamitonians for each configurations. The lambda and vee type
configurations are exactly solved with different initial conditions while
taking the two-mode classical and quantized fields . For the classical field,
it is shown that the Rabi oscillation of the lambda model is similar to that of
the vee model and the dynamics of the vee model can be recovered from lambda
model and vice versa simply by inversion. We then proceed to solve the
quantized version of both models introducing a novel Euler matrix formalism. It
is shown that this dynamical symmetry exhibited in the Rabi oscillation of two
configurations for the semiclassical models is completely destroyed on
quantization of the field modes. The symmetry can be restored within the
quantized models when the field modes are both in the coherent states with
large average photon number which is depicted through the collapse and revival
of the Rabi oscillations.
