  We generalize the kinetic theory of fluids, in which the description of
fluids is based on the geodesic motion of particles, to spacetimes modeled by
Finsler geometry. Our results show that Finsler spacetimes are a suitable
background for fluid dynamics and that the equation of motion for a
collisionless fluid is given by the Liouville equation, as it is also the case
for a metric background geometry. We finally apply this model to collisionless
dust and a general fluid with cosmological symmetry and derive the
corresponding equations of motion. It turns out that the equation of motion for
a dust fluid is a simple generalization of the well-known Euler equations.
