Abstract: A flexible counter for an embossing system provides resilient support under a sheet which opposes pressure from a contoured die forming an embossment in the sheet. The flexible counter includes a resilient mat and a fixed bolster which supports the mat. The bolster has a peripheral wall which extends around sides of the mat so that an upper portion of the mat protrudes above the peripheral wall. In addition, the bolster includes support surfaces bounded by recesses. The support surfaces support a bottom surface of the mat, and the recesses receive bulging portions of the mat when compressed under pressure from the die.