  The notion of a delta shock wave and a singular shock wave was introduced and
employed by different authors, and it was shown that a large class of Riemann
problems can be solved globally with these additional building blocks. The aim
of this paper is to study the interaction of one type of these new solutions,
the delta shock waves, with the classical types of solutions. Our model problem
is $2 \times 2$ system derived from a simplified model of
magneto-hydrodynamics.
  The solution concept used in the present paper can be simply described as
analogous to the standard one but with $L^{\infty}$-functions substituted by
measures in one component of a solution. Here, the delta function is
represented by so called two sided delta function.
  We shall mention only two specific details from the complete interaction
result. In some situation the interaction result may contain
non-overcompressible delta shock wave called delta contact discontinuity.
During delta shock and rarefaction wave interaction it may happen that some
$L_{loc}^{1}$-function appear.
