This thesis presents the modeling of radio and X-ray emissions from supernova (SN) shock fronts and hydrodynamical simulations of SN-circumstellar medium (CSM) interaction. The interaction of SN ejecta with the CSM drives a strong shock wave into the CSM. These shocks are ideal places where effective particle acceleration and magnetic field amplification can take place. The accelerated relativistic particles, in the presence of magnetic field, could emit part of their energy via synchrotron radiation in radio wavelengths. The flux of this radiation, when compared with observations, gives an estimate of the CSM density. This could either be the particle density (n_ISM) in case of the SN exploding in a constant density medium, characteristic of interstellar medium, or pre-SN mass loss rate (dM/dt) of the progenitor system for a wind medium. In Paper I we have modeled the synchrotron emission and compared that with the radio upper limits measured for the Type Ia SNe 2011fe and 2014J. Assuming equipartition of energy between electric and magnetic fields, with 10% of the thermal shock energy in each field, we obtain a very low density medium, having n_ISM <~ 0.35 cm^-3, around both the SNe. In terms of dM/dt this implies an upper limit of 10^-9 M_sun yr^-1 for a wind velocity, v_w, of 100 km s^-1. This study suggests that in SN shocks it is more likely that the amplification efficiency of magnetic fields is less than that for the electric fields. In Paper II, we carry out the hydrodynamical simulations of the interaction between SN ejecta and CSM for SN 1993J and SN 2011dh. Subsequently, the radio and X-ray emission have been calculated from the shocked gas encapsulated between the forward and reverse shocks. Considering the ejecta profile of these SNe from multi-group radiation hydrodynamics simulation (STELLA), it is found from our investigation that for a wind velocity of 10 km/s around 6500 years prior to the explosion of SN 1993J a change in mass loss rate occurred in the system. For a binary system this may imply that the change in dM/dt could be due to a change in the mass accretion efficiency of the companion star. In case of SN 2011dh the late time emission is turned up to be consistent with a wind medium with (dM/dt)/v_w = 4 × 10^-6 M_sun yr^-1/10 km s^-1. Paper III focuses on the radio emission from four young SNe Type Ia, SN 2013dy, SN 2016coj, SN 2018pv and SN 2018gv. Using the same model for radio emission as in Paper I, the upper limits on dM/dt and n_ISM are estimated. We found tenuous media around these SNe, which put tight constrain on their progenitor systems.