The invention relates to a cup package made of a fiber-based material, such as polymer-coated packaging board, comprising a cup (1) containing a packaged product (2) and a lid (6) closing the mouth of the cup. In accordance with the invention, the cup (1) has a collar (5) bent downwardly from the mouth of the cup and diverging from the cup skirt (3), and the lid (6) has a rim (8) oriented accordingly downwardly from the collar, the lid being fixed in position by heat-sealing between said collar and rim parts. For opening the package, the lid (6) can be equipped with a tear strip (11) surrounding its rim (8). In addition, the lid (6) may be nested with the cup (1), so that compression and friction between their opposite surfaces retain the lid in position in the reclosed package.