The propagation of slow magnetoacoustic waves along a multithreaded coronal loop is modelled analytically by means of a ray tracing method. It is shown how cross field gradients build up due to phase mixing. The cross field gradients can enhance shear viscosity so that it dominates over compressive viscosity. Nevertheless the short dissipation distances (similar to 10(7) m) observed for slow waves in coronal loops require very small cross field length scales which imply a filamentary structure on scales at least three orders of magnitude below the current detection limit of TRACE and close to the limit where magnetohydrodynamic (MHD) theory breaks down. The observed dissipation distances can alternatively be explained by phase mixing in its ideal regime, where the apparent damping is due to the spatial integration of the phase mixed amplitudes by the observation.