A process for preparing extruded polymeric foam comprising the following steps: a. providing a foamable polymer composition in an extruder at an initial temperature and an initial pressure, the foamable polymer composition comprising a blowing agent and a polymer matrix that comprises a polymer component with a softening temperature, the initial temperature exceeding the softening temperature of the polymer component and the initial pressure high enough to preclude foaming of the foamable polymer composition; and b. extruding the foamable polymer composition in an extrusion direction into an atmosphere at a pressure below the initial pressure and allowing the foamable polymer composition to expand into a polymeric foam prior to cooling to a temperature below the softening point of the foamable polymer composition, wherein the "pressure below the initial pressure" is atmospheric pressure; wherein prior to cooling to a temperature below the softening point in step (b), the foamable polymer composition expands with a thickness expansion ratio of at least 30:1 while traveling through and contacting opposing forming plates that provide at least two sequential constraining sections along the extrusion direction, the forming plates in each constraining section comprising essentially parallel constraining walls that restrict expansion of the foamable polymer composition in a thickness dimension and wherein the constraining section closest to the extruder has essentially parallel walls defining a spacing in the thickness dimension that is smaller than the spacing of parallel walls defining the second constraining section; and wherein the polymer composition expands into a polymeric foam having a thickness of 10 centimeters or more and essentially uniform density and compressive strength profiles along the thickness dimension of the polymeric foam; wherein "essentially parallel" means that the distance between two forming walls at any two points on a forming wall is either equal or the smaller distance is within 5% of the larger distance; wherein essentially uniform density profile along the thickness dimension of the foam is determined by cutting the foam into 10-12 millimeter thick layers perpendicular to the thickness dimension, maintaining the length and width dimension in each layer, and measuring the density for each layer according to the method of ISO 845-95, wherein the combination of density values for all of the layers represents the density profile along the thickness dimension for the foam, and deviations in density between layers represent deviations along the thickness dimension, and wherein the extruded polymeric foam has an essentially uniform density profile along its thickness dimension if the difference between the density of any one layer from the average density of the maximum and minimum densities is less than 5% of the average density of the maximum and minimum densities; and wherein essentially uniform compressive strength along the thickness dimension of the foam is determined in similar manner as the density profile except that 15 millimeter thick layers are used, and compressive strength is measured in the thickness dimension, i.e., the 15 millimeter dimension, according to the method of EN-826 for each layer; wherein the combination of compressive strength values for all of the layers represents the compressive strength profile along the thickness dimension for the foam; wherein deviations in compressive strength between layers represent deviations along the thickness dimension; and wherein the extruded polymeric foam is deemed to have an essentially uniform compressive strength profile along its thickness dimension if the difference between the compressive strength of any one layer from the average compressive strength of the layers having the highest and lowest compressive strengths is less than 10%, preferably 9% or less, still more preferably less than 9% of the average compressive strength of the maximum and minimum compressive strengths. a. providing a foamable polymer composition in an extruder at an initial temperature and an initial pressure, the foamable polymer composition comprising a blowing agent and a polymer matrix that comprises a polymer component with a softening temperature, the initial temperature exceeding the softening temperature of the polymer component and the initial pressure high enough to preclude foaming of the foamable polymer composition; and b. extruding the foamable polymer composition in an extrusion direction into an atmosphere at a pressure below the initial pressure and allowing the foamable polymer composition to expand into a polymeric foam prior to cooling to a temperature below the softening point of the foamable polymer composition, wherein the "pressure below the initial pressure" is atmospheric pressure;