  The shear shallow water model is a higher order model for shallow flows which
includes some shear effects that are neglected in the classical shallow models.
The model is a non-conservative hyperbolic system which can admit shocks,
rarefactions, shear and contact waves. The notion of weak solution is based on
a path but the choice of the correct path is not known for this problem. In
this paper, we construct exact solution for the Riemann problem assuming a
linear path in the space of conserved variables, which is also used in
approximate Riemann solvers. We compare the exact solutions with those obtained
from a path conservative finite volume scheme on some representative test
cases.
