Cover device for a drink container, the cover device comprising: a basic assembly having a drink opening and a ring-shaped member; a valve arrangement comprising a valve element having a central portion and an outer ring-shaped portion which are connected to each other through an area of the valve element at a position where the valve element is hingably associated with the basic assembly through contact to the ring-shaped member, wherein only the central portion of the valve element is in direct communication with the drink opening of the basic assembly, and wherein sizing, positioning and orientation of the portions (27, 28) of the valve element are realized for having a smaller total moment of force on the central portion of the valve element than on the outer ring-shaped portion of the valve element when the valve element is subjected to pressure from the side of the cover device which is intended to face the drink container, whereby the valve element comprises a sleeve, a circumference of the sleeve being substantially similar to a circumference of the ring-shaped member; wherein a slit is located inside the sleeve, in the central portion of the valve element, the sleeve and the ring-shaped member having a first diameter in the direction of the slit and a second diameter perpendicular to the slit, and wherein a ratio between the first and second diameters of the sleeve, before assembly of the sleeve and the ring-shaped member, is smaller than a ratio between the first and second diameters of the ring-shaped member, such that during assembly of the valve element and the basic assembly, the sleeve encloses or is enclosed by the ring-shaped member and is stretched or widened along the first diameter, and compressed or narrowed along the second diameter. a basic assembly having a drink opening and a ring-shaped member; a valve arrangement comprising a valve element having a central portion and an outer ring-shaped portion which are connected to each other through an area of the valve element at a position where the valve element is hingably associated with the basic assembly through contact to the ring-shaped member, wherein only the central portion of the valve element is in direct communication with the drink opening of the basic assembly, and wherein sizing, positioning and orientation of the portions (27, 28) of the valve element are realized for having a smaller total moment of force on the central portion of the valve element than on the outer ring-shaped portion of the valve element when the valve element is subjected to pressure from the side of the cover device which is intended to face the drink container, whereby the valve element comprises a sleeve, a circumference of the sleeve being substantially similar to a circumference of the ring-shaped member; wherein a slit is located inside the sleeve, in the central portion of the valve element, the sleeve and the ring-shaped member having a first diameter in the direction of the slit and a second diameter perpendicular to the slit, and wherein a ratio between the first and second diameters of the sleeve, before assembly of the sleeve and the ring-shaped member, is smaller than a ratio between the first and second diameters of the ring-shaped member, such that during assembly of the valve element and the basic assembly, the sleeve encloses or is enclosed by the ring-shaped member and is stretched or widened along the first diameter, and compressed or narrowed along the second diameter.