  We examine the buckling shape and critical compression of confined
inhomogeneous composite sheets lying on a liquid foundation. The buckling modes
are controlled by the bending stiffness of the sheet, the density of the
substrate, and the size and the spatially dependent elastic coefficients of the
sheet. We solve the (linearized) F\"oppl-von K\'arm\'an equations describing
the mechanical equilibrium of a sheet when its bending stiffness varies
parallel to the direction of confinement. The case of a homogeneous bending
stiffness exhibits a degeneracy of wrinkled states for certain sizes of the
confined sheet. This degeneracy disappears for spatially dependent elastic
coefficients. Medium length sheets buckle similarly to their homogeneous
counterparts, whereas the wrinkled states in large length sheets localize the
bending energy towards the soft regions of the sheet.
