A cover plate system for a gap (15) between two structural members (10, 20) is provided. The system includes an elongated cover (30) that extends across the gap (15) from a first structural member (10) to a second, spaced-apart structural member (20). The cover plate system further includes damped spring anchors (40) for engaging the cover plate (30) to an underlying structural member (10) and dampers (50, 60) for absorbing energy imparted to the cover plate (30) by vehicular traffic. The cover plate system minimizes the strain energy that is absorbed by the cover plate (30), which results in less cover plate slapping and bouncing during operation.