Materials with negative Poisson's ratios (auxetic materials) have several advantages compared to conventional materials, including increased plane strain fracture resistance and increased shear modulus. A method for the manufacture of honeycomb ceramics with a structure, which yields negative Poisson's ratio is described. Ceramics with cellular or honeycomb structures have applications as substrates in catalytic converters for the emissions from internal combustion engines. In such devices due to the extreme temperature variations, the structure has to provide high thermal shock resistance. It is possible to increase the thermal shock resistance by incorporating specific web geometries, Such structures can absorb or compensate for compressive and tensile stresses generated in the body during thermal expansion and contraction. It is shown that such structures can be produced by the extrusion of ceramic pastes through polymer dies produced by rapid prototyping (selective laser sintering), CAD technology was used to design the die. A ceramic paste based on a zirconia powder was used to make the cellular extruded tube. The negative Poisson's ratio behaviour was confirmed by employing a simple test.