A packer, and operation of the same, which forms elastomeric seals and non-elastomeric seals. The packer may be constructed from a non-elastomeric tubular core having a frustoconical shaped inner diameter. The outer diameter of the core may be substantially smooth and carry one or more elastomeric sealing elements. The packer is set by causing the diametrical expansion of the tubular core. The construction of the tubular core is preferably such that its diametrical expansion causes the formation of radial raised portions (upsets) on the outer surface. These raised portions form the non-elastomeric seals and also prevent extrusion of the elastomeric sealing elements.