  We model the circumstellar medium with four density profiles: hyperbolic
type, power law type, exponential type and Gaussian type. We solve analytically
or numerically the four first-order differential equations which arise in the
framework of the classical thin layer approximation. The non-cubic dependence
of the swept mass with the advancing radius is also considered. We derive the
equation of motion for the thin layer approximation in special relativity in
two cases. The initial conditions are chosen in order to model the temporal
evolution of SN 1987A over 23 years and of SN 1006 over 1000 years. We review
the building blocks of the symmetrical and asymmetrical formations of the
image.
