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Key relationships between foam morphologies and melt‐state rheological parameters are here exposed for biobased poly(butylene‐succinate) (PBS) and standard petrobased polyethylene (PE) foams processed by single‐screw extrusion. Scanning electron microscopy followed by image analysis revealed cell diameters and densities in the range of 250–700 µm and 3–4.104 cells/cm3, respectively. PBS and PE have similar morphologies except for cell diameters which are slightly higher for PBS foams. The melt index roughly controls foam microstructures but deeper insights are obtained through correlations with shear/extensional rheology experiments. In particular, the melt strength and the strain hardening control the cell growth mechanisms. Concerning the cell density, the shear viscosity in the die plays a key role and agreements with nucleation theories can be discussed based on simulated pressure–velocity profiles using finite element software. In our extrusion conditions, the residence time comes out to have a crucial role with distinct behaviors between PE and PBS indicating a potential modification of the polymer/CO2 interfacial tension. Consequently, an accurate control of the foam morphology seems achievable via a careful selection of the polymer grades and PBS represents a promising alternative to PE for further developments of biobased foams. POLYM. ENG. SCI., 58:503–512, 2018. © 2017 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]