In   high-contrast composite materials, stress concentration occurs in the narrow   regions between adjacent hard inclusions as they approach close proximity.   Significant progress has been made over the past two decades in understanding   such concentration phenomenon. Recently, the singularities of higher-order   derivatives of solutions for the Lam\'e system and the Stokes equations in   between closely spaced inclusions are both derived. In this talk we will demonstrate   how gradient estimates derived for the electrostatic equation and the Lam\'e   system can be extended to analyze resonant interactions in systems of multiple   closely spaced acoustic subwavelength resonators and subwavelength elastic   resonators.