Wrinkling patterns in thin elastic sheets typically involve oscillations on increasingly fine length scales, making the characterization of limiting configurations a challenging variational problem.  In this talk I consider the classical Lamé problem for a stretched elastic annulus within the Föppl–von Kármán theory. After subtracting the relaxed membrane energy and rescaling appropriately, I establish a Γ-convergence result towards a convex measure-valued functional describing the distribution of wrinkle frequencies. The limiting model provides a rigorous effective description of wrinkling patterns and yields existence and qualitative properties of optimal frequency distributions. The work is motivated by the previous analysis of Bella and Kohn.