Prepare extruded thermoplastic polymer foam by preparing a foamable polymer mixture containing thermoplastic polymer and blowing agent at a mixing pressure, cooling the foamable polymer mixture and extruding it through a foaming die at a die pressure at least 90 bars lower than the mixing pressure and out through a die opening having cross sectional dimensions of 2.5 millimeter or more and a cross sectional area of at least 700 square millimeters at a flow rate greater than 500 kilograms per hour and allow it to expand into a polymer foam between shaping elements while restraining the extrusion rate with a restraining device so as to form polymer foam having 96 volume percent or less void volume, anisotropic cell size, a thickness of 50 millimeter or greater, compressive and tensile moduli in the thickness dimension greater than 35 mega pascals and an average shear modulus greater than 16 mega pascals.