To enable the front of a cover body to be pushed up to an appropriate height with a hook disengaged by pushing of a push button for a cover-equipped case which has a mechanism wherewith the hook dangling from the front of the cover body is disengaged from an engagement protuberant stripe provided at the front of the case main body when the push button provided at the front wall of the case main body is pushed in and the cover body is turned round a hinge part at the rear of the case and moved upward for opening.

A vertically-moving member 41 is attached, being urged to move downward, to the front of the cover body 21. The engagement protuberant stripe 14 provided transversely at the front of the upper end of the rear wall 13 of the push button is retreated when the push button 11 slidably fitted into a traverse hole 7 provided at the front of the case main body is pushed rearward, and the hook 30 dangling from the front of the cover body and engaged with the underside of the engagement protuberant stripe is disengaged, and thereby the vertically-moving member 41 pushes the front of the cover body upward until an engagement protuberance 31 comes into contact with the underside of a traverse frame part 44a.