  We examine the existence of shock profiles for a hyperbolic-elliptic system
arising in radiation hydrodynamics. The algebraic-differential system for the
wave profile is reduced to a standard two-dimensional form that is analyzed in
details showing the existence of heteroclinic connection between the two
singular points of the system for any distance between the corresponding
asymptotic states of the original model. Depending on the location of these
asymptotic states, the profile can be either continuous or possesses at most
one point of discontinuity. Moreover, a sharp threshold relative to presence of
an internal absolute maximum in the temperature profile --also called {\sf
Zel'dovich spike}-- is rigourously derived.
