The preparation, rheological behavior, and solution properties of branched poly(3-hydroxy butyrate)-co-(3-hydroxy valerate), PHBV, are described. Branching is produced by the use of dicumyl peroxide (DCP) during the reactive extrusion of PHBV. The shear viscosities of reactively extruded PHBV and the straight-chain polymer of similar molecular weight are nearly identical, but the reactively extruded PHBV's elongational viscosity is considerably higher. High elongational viscosity of these polymers results from a branched structure produced when extrusion is carried out in the presence of small amounts of DCP (0.025-0.3 wt %). Strain hardening is observed in the elongational response of the branched PHBV at all deformation rates and increases with increasing concentrations of DCP. Study of the solution properties of the linear and branched PHBV indicates larger hydrodynamic volume compared to that of polystyrene of comparable molecular weight. Mark-Houwink plots, observed for PHBV, exhibited increasing nonlinearity with increasing DCP content. Trifunctional branching frequencies computed on the basis of intrinsic viscosity ratios indicated explosive growth in branching, possibly due to the generation of microgel, when branching reactions are initiated with a DCP level exceeding 0.2 wt %.