This paper reports work on extrusion foaming of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) with a chemical blowing agent based on sodium bicarbonate and citric acid and calcium carbonate nucleation agent. It includes investigations in the effects of rheological behaviour of the polymer, blowing agent, nucleation agent and processing conditions on the foam density and morphology. The poly(3-hydroxybutyrate-co-3-hydroxyvalerate) is a natural biodegradable polyester with high crystallinity, low melt viscosity and slow crystallisation rate and high sensitivity to the thermal degradation at temperatures above its melting point, making it particularly difficult to control the foaming process. Use of negative gradient temperature profile was found beneficial to minimise the thermal degradation and achieve necessary melt strength to stabilise the cell structure. Solidification of the super-cooled polymer melt occurring at the die was discussed in relation to the selection of the temperature profile and rheological behaviour and solidification of the poly(3-hydroxybutyrate-co-3-hydroxyvalerate) characterised by rotational rheometry. In addition to extrusion foaming conditions, effect of the blowing and nucleation agents on rheology of the polymer, the cell refinement on foam density and morphology were discussed. The poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was extruded with a twin screw extruder fitted with a strand die yielding up to 60% density reduction with uniform fine cell structure.