A handle structure includes a handle panel; a strap handle disposed below the handle panel and extending along a notional longitudinal line extending between the end edges of the handle panel; a handle opening defined in the handle panel, the handle opening being disposed in registry with at least part of the strap handle such that the at least part of the strap handle may be raised and extend through the handle opening when the strap handle is moved to a used position wherein the at least part of the strap handle is disposed above the handle panel; and at least one tear resisting cut line in the handle panel, the at least one tear resisting cut line extending from the handle opening toward an adjacent one of the side edges of the handle panel.