We show the results of the broad-band optical polarization monitoring carried out for SN2006aj and SN2008D. The final goal is to infer information from the still uncertain geometric expansion of the SNe associated to GRBs. We discuss on the polarimetric differences between these two explosive events, and their possible correlation with their spectral type. In the particular case of SN2008D the existence of SN2007uy in the same host galaxy (NGC2770) allowed us also to compare the polarimetric properties of a hypernova and a "standard" supernova. We also discuss on the limitations imposed by the host galaxy dust on our polarimetric measurements.