The radio non-detection of two Type Ia supernovae (SNe) SN 2011fe and SN 2014J has been modeled considering synchrotron radiation from shock accelerated electrons in the SN shock fronts. With 10% each of the bulk kinetic energy in electric and magnetic fields, a very low density of the medium around both the SNe has been estimated from the null detection of radio emission, around 1 and 4 years after the explosion of SNe 2014J and 2011fe, respectively. Keeping the fraction of energy in electrons fixed at 10%, a medium with particle density ~ 1cm−3 is found when 1% of the post shock energy is in magnetic fields. In case of a wind medium, the former predicts the mass loss rate Ṁ to be <10−9
⊙ yr−1, and the latter gives an upper limit ~10−9
⊙ yr−1, for wind velocity of 100 kms−1, for both the SNe. The tenuous media obtained from this study favor the double degenerate as well as a spin up/down model for both SNe 2011fe and 2014J.