A rotary anvil cutting mat comprising: na generally elongate body defining an axial length and a circumferential length, nsaid body having: nopposing first and second circumferential edges; and nopposing first a second axial edges, each arranged to have a nonlinear configuration when measured across the entirety of said axial length; na first end portion proximate said first axial edge having a first locking member, said first locking member arranged to be received between a first sidewall and a locking wedge of a channel lockup device; na second end portion proximate said second axial edge having a second locking member, wherein said cutting mat is wrappable into a generally cylindrical shape such that said first and second locking members abut in mating nrelationship, said second locking member further abuts said locking wedge opposite said first locking member, and said first and second axial edges define a seam therebetween.