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
