A method of making an auxetic mesh, which method includes: (a) extruding a polymeric material 60 onto an open casting surface 58 that has an intended pattern 62 disposed therein, the pattern 62 being configured to create an auxetic mesh 20; (b) wiping off excess extruded polymeric material 60 from the open casting surface 64; (c) removing the cast mesh 20 from the open casting surface 64 after the excess polymeric material 60 has been wiped off; and (d) removing any residual polymeric material that is not of the intended mesh pattern 20. The method allows for the continuous production of auxetic meshes.