We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. The system is a simplification of a recently propose system of five conservations laws by Bouchut and Boyaval that models viscoelastic fluids. An important issue is that the considered 3 × 3 system is such that every characteristic field is linearly degenerate. We study the Riemann problem for this system and under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta-shock type solutions are established.