Abstract: The invention deals with a thin-walled compressible package where on the compressible package transversal recesses are created so that the recesses are created at least in four layers where in each layer there are at least two recesses and at the same time the recesses in one layer are always in the position under and/or over the contact place of the recesses created in the neighbouring layers or under and/or over the gap between the recesses created in the neighbouring layers while at the same time the recesses in the neighbouring layers partly overlap each other with their side mains with regard to the longitudinal axis from the axial point of view, while at the same time at least two types of recesses, having different profiles and/or depths are created, and where the side margins of at least the principal recesses in the transversal direction to the longitudinal axis of the package consist of the transition of the profile of the recess to the flat surface of the package or of the transition of the profile