In the literature it is well known that foaming is a highly complex process which is influenced by e.g. the process parameters, the choice of polymer and its structure as well as by the blowing agent type and concentration. Due to the dependency of both shear and elongational viscosity on such influencing factors, the melt viscosity is highly influenced during the foaming process. The viscosity therefore is a crucial parameter for the foaming process itself. A collapse of single bubbles or even of the whole foam structure is often a result of a too low elongational viscosity and the associated melt strength. That’s why polylactide (PLA) is difficult to foam. In this study the melt viscosity in shear and elongation as well as the melt strength was increased by modifying PLA with dicumyl peroxide on a twin-screw extruder. Thus, the structure was changed from linear to branched and strain hardening was observed during uniaxial measurements with a Sentmanat extension rheometer at different temperatures and deformation rates. By use of the molecular stress function model (MSF-model) the uniaxial elongational viscosity of the modified PLA including the observed strain hardening at different temperatures and deformation rates was predicted. Through the good accuracy of the MSF-model predictions in comparison to the uniaxial measurements, the equibiaxial viscosity was also modeled with the MSF-model since equibiaxial deformations mainly occur during the foaming process. Because of the good accuracy of the MSF-model, the elongational viscosity of modified polymers for foaming applications can be characterized, predicted and thus used e.g. for bubble growth simulations.