Magnetohydrodynamic (MHD) kink waves have been observed frequently in the solar coronal flux tubes which makes
them a great tool for the seismology of the solar corona. Here, the effect of viscosity is studied on the evolution of
kink waves. To this aim, we solve an initial value problem for the incompressible linearized viscous MHD equations
in a radially stratified flux tube in the limit of long wavelengths. Using a modal expansion technique, the spatiotemporal
behavior of the perturbations is obtained. We show that the viscosity suppresses the rate of phase-mixing
of the perturbations in the inhomogeneous region of the flux tube and prevents building up of small scales in the
system. The viscous dissipation function is calculated to investigate plasma heating by viscosity in the inhomogeneous
layer of the flux tube