How does the Geometry of the column effect the Post Buckling shape? I
am concerned about the post bucling shape and not the stress etc, as
it is elastic and not for failure analysis. Also The columns are
actually, thing sheet of metal under compressive loading, so may be
they are beams under compressive loads!!

Well, regarding post buckling shapes, you have the Euler Buckling
load, P_e = Pi^2*E*I/L^2 where E is the modulus of elasticity, L is
the member length, and I is the cross sectional moment of inertia.

Depending how your column is supported, i.e. a pinned-pinned column, a
cantilever column, etc, you get P_buckling = C*P_e, where C is a
number that can be derived by looking at the initial conditions and
solving.  For a cantilever column, for instance, C = 1/4.

Note that I depends entirely on the column geometry.  L, your column
length would also be a function of column geometry.

Differences in I and L will affect when your member starts to buckle,
which obviously affect the post buckling shape.

A further thought - your comment regarding thin sheets of metal being
equal to beams under compressive loads is a no no.

Typical buckling theory differentiates between shallow and deep beams,
and there are unique equations for both.  There are also entirely
separate equations for plates and shells.

Treating a thin sheet of metal like a column may give you a reasonable
first order approximation of buckling, but will ultimately yield an
incorrect answer.  Look into plate and shell buckling for better
solutions.