The present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient have been analysed. Two types of caps (for example, concave upwards and concave downwards) have been considered for the numerical results. The effect of the concavity on added mass and damping coefficient has also been studied. The present study should be helpful to understand the nature of waves generated by a heaving submerged body in an ice-covered ocean. © 2020 Oxford University Press. All rights reserved.