  In this paper we study the one-dimensional Riemann problem for a new
hyperbolic system of three conservation laws of Temple class. This systems it
is a simplification of a recently propose system of five conservations laws by
Bouchut and Boyaval that model viscoelastic fluids. An important issues is that
the considered $3 \times 3$ system is such that every characteristic field is
linearly degenerate. Then, in despite of the fact that it is of Temple class,
the analysis of the Cauchy problem is more involved since general results for
such a systems are not yet available. We show a explicit solution for the
Cauchy problem with initial data in $L^\infty$. We also study the Riemann
problem for this system. Under suitable generalized Rankine-Hugoniot relation
and entropy condition, both existence and uniqueness of particular delta-shock
type solutions are established.
