  Here we extend the conservation of energy in the framework of the thin layer
approximation to the asymmetrical case. Four types of interstellar medium are
analysed, in which the density follows an inverse square profile, a power law
profile, an exponential profile and a toroidal profile. An analytical solution
for the radius as a function of time and the polar angle in spherical
coordinates is derived in the case of the inverse square profile. The
analytical and numerical results are applied to two supernova remnants: SN
1987A and SN 1006. The back reaction due to the radiative losses is evaluated
in the case of the inverse square profile for the surrounding medium. Two
models for the image formation are presented, which explain the triple ring
visible in SN 1987A and the jet feature of SN 1006.
