Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Recent observations by Hinode/SOT showed that the spicules mostly exhibit upward propagating high frequency waves. Here we investigate the dissipation of such waves due to phase mixing in stratified environment of solar spicules. Since they are highly dynamic structures with speeds at about significant fractions of the Alfvén phase speed, we take into account the effects of steady flows. Our numerical simulations show that in the presence of stratification due to gravity, damping takes place in space than in time. The exponential damping low, , is valid under spicule conditions, however the calculated damping time is much longer than the reported spicule lifetimes from observations.