We present exact analytical solutions for the electric and magnetic fields in continuously graded models of flat lenses. We model the lenses as compact composites with continuously varying permittivity and permeability functions, which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the application of the proposed procedure by obtaining exact analytical solutions for the electric and magnetic fields for a class of composite designs with constant permeability (μ = μ0) and radially graded permittivity.