  Given the recent interest in magnetohydrodynamic (MHD) waves in pores and
sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by
modeling solar photospheric waveguides with a cylindrical inhomogeneity
comprising a uniform interior, a uniform exterior, and a continuous transition
layer (TL) in between. Performing an eigen-mode analysis in linear, resistive,
gravity-free MHD, our approach is idealized in that, among other things, our
equilibrium is structured only in the radial direction. We can nonetheless
address two damping mechanisms simultaneously, one being the Ohmic resistivity,
and the other being the resonant absorption of SSKMs in the cusp and
Alfv$\acute{\rm e}$n continua. We find that the relative importance of the two
mechanisms depends sensitively on the magnetic Reynolds number ($R_{\rm m}$).
Resonant absorption is the sole damping mechanism for realistically large
values of $R_{\rm m}$, and the cusp resonance in general dominates the
Alfv$\acute{\rm e}$n one unless the axial wavenumbers are at the lower end of
the observationally relevant range. We also find that the thin-boundary
approximation holds only when the TL-width-to-radius ratios are much smaller
than nominally expected. The Ohmic resistivity is far more important for
realistically small $R_{\rm m}$. Even in this case, SSKMs are only marginally
damped, with damping-time-to-period-ratios reaching $\sim 10$ in the parameter
range we examine.
