Isotropic and anisotropic shape‐memory polymer foams are prepared by supercritical carbon dioxide foaming from a multiblock copolymer (PDLCL) consisting of poly(ω‐pentadecalactone) and poly(ε‐caprolactone) segments. Analysis by micro‐computed tomography reveals for the anisotropic PDLCL foam cells a high shape anisotropy ratio of R = 1.72 ± 0.62 with a corresponding Young's compression moduli ratio between longitudinal and transversal direction of 4.3. The experimental compression data in the linear elastic range can be well described by the anisotropic open foam model of Gibson and Ashby. A micro‐morphological analysis for single pores using scanning electron microscopy images permits the correlation between the macroscopic stress‐compression behavior and microscale structural changes.