This study investigates the heaving motion of an elliptic disc submerged in deep water under an ice-covered ocean, using linear water wave theory. By applying Green’s integral theorem, the problem is transformed into a two-dimensional hypersingular integral equation with a hypersingular kernel on the surface of the elliptic disc in terms of the velocity potential difference and is then solved numerically using an expansion collocation method. Validation is achieved by comparing the numerical results with published data for a circular disc before extending the analysis to a submerged elliptic disc in the presence of an ice cover. The added mass and damping coefficients are computed and graphically depicted as functions of the wave number for various submerged depths, aspect ratios of the semi-major to semi-minor axis and flexural rigidity of the ice cover to investigate their influence. The numerical results exhibit higher added mass and damping coefficients for smaller submergence depths of the body and a higher ratio of the semi-major axis to the semi-minor axis. Additionally, the flexural rigidity of the ice cover significantly impacts the dynamic response of the submerged disc, underscoring its critical role in the system’s behavior. This study provides valuable insights into the flow physics influenced by a rigid elliptic disc beneath an ice-covered surface, examining interactions and dynamics to advance applications in ice environments.