  In this paper hyperbolic partial differential equations with random
coefficients are discussed. Such random partial differential equations appear
for instance in traffic flow problems as well as in many physical processes in
random media. Two types of models are presented: The first has a time-dependent
coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random
field coefficient with a given covariance in space. For the former a formula
for the exact solution in terms of moments is derived. In both cases stable
numerical schemes are introduced to solve these random partial differential
equations. Simulation results including convergence studies conclude the
theoretical findings.
