This paper addresses the influence of the polymer rheology on cell nucleation and growth in biobased poly(butylene succinate) (PBS) foams produced by single-screw extrusion in the presence of an endothermic blowing agent. Various poly(ethylene) (PE) grades were also tested as model materials. Foam morphologies were observed and characterized by scanning electron microscopy followed and image analysis. Similar foam densities are obtained around 0.4 g/cm 3 and the cell density can be tuned between 5.10 4 and 1.4.10 5 cells/cm 3. Based on polymer melt rheology and nucleation theories, the relationship between experimental cell density and simulated pressure profiles in the die computed using a commercial finite element software package were discussed. Low-density PE with branched architectures tends to favor a uniform cell size thanks to strain-hardening phenomenon. Thus, an accurate control of the foam morphology seems possible by tuning the polymer macromolecular architecture. An extrapolation of this result was made to three PBS commercial grades. The PBS grade with the highest melt viscosity and crystallization rate is the only one displaying promising features in terms of cell density and cell size. Consequently, the development of foamable PBS grades with tailored morphologies still requires extensive modifications of macromolecular architectures and precise tuning of rheological parameters to meet the requirements of number of industrial applications and enlarge the accessible markets.