A method and apparatus for manufacturing a catalytic converter is described where the catalytic converter is comprised of an outer tube member having a monolith substrate internally compressed therein with a wrapped mat material surrounding the monolith substrate and intermediate the outer tube. One or more monolith members can be applied within the outer tube and heat shields may also be applied internal to the outer tube and adjacent to the monolith substrate. The assembly of the catalytic converter includes measuring the sequence of compression of the mat material to the monolith substrate in order to understand the possible force characteristics that can be applied during the assembly thereof. The mat material is therefore compressed within the outer tube by way of compression jaws, by compression rollers, by spinning and/or by a shrinker including compression members. The compression of the mat material can be in single or multiple steps.