A resiliently deformable containment structure having an open bottom end and a raised center portion. A central hub, situated centrally in a textile containment sheet, is provided. A plurality of elongate inflatable beam members are arranged circumferentially around the central hub, each extending radially outwardly and in a downwardly-extending manner therefrom and each underlying or overlying the textile containment sheet to support, when inflated, the textile containment sheet in a downwardly-extending shape to form an enclosure having an open bottom end. Distal ends of the inflatable beam members are tethered to one or more anchor members situated below the open bottom end of the dome structure. The structure is suited for placement above and over a compromised sub-sea structure for collecting and recovering to surface fluids which may be leaking therefrom. A method for containing and recovering such fluids from a compromised sub-sea structure is further disclosed.