Solutions of the wave equation in a geometry with stochastic ray trajectories have been considered. In particular we have studied the fast magnetosonic wave in the limit of weak damping. It is found that the often used assumption of a uniform wave energy density in the phase space for stochastic wave solutions does not hold, a conclusion which should be valid not only for applications related to wave propagation in plasmas. A new wave field model for stochastic fields has been obtained for tori with nearly circular cross sections.