  The shallow-water equations of Saint-Venant, often used to model the
long-wave dynamics of free-surface flows driven by inertia and hydrostatic
pressure, can be generalized to account for the elongational rheology of
non-Newtonian fluids too. We consider here the $4 \times 4$ shallow-water
equations generalized to viscoelastic fluids using the Johnson-Segalman model
in the elastic limit (i.e. at infinitely-large Deborah number, when source
terms vanish). The system of nonlinear first-order equations is hyperbolic when
the slip parameter is small $\zeta \le 1/2$ ($\zeta$ = 1 is the corotational
case and $\zeta = 0$ the upper-convected Maxwell case). Moreover, it is
naturally endowed with a mathematical entropy (a physical free-energy). When
$\zeta \le 1/2$ and for any initial data excluding vacuum, we construct here,
when elasticity $G > 0$ is non-zero, the unique solution to the Riemann problem
under Lax admissibility conditions. The standard Saint-Venant case is recovered
when $G \to 0$ for small data.
