  In this study we explore the possibility of simplifying the modeling of
magnetohydrodynamic (MHD) slow body modes observed in photospheric magnetic
structure such as the umbrae of sunspots and pores. The simplifying approach
assumes that the variation of the eigenvalues of slow body waves can be derived
by imposing that the longitudinal component of velocity with respect to the
tube axis is zero at the boundary of the magnetic flux tube, which is in a good
agreement with observations. To justify our approach we compare the results of
our simplified model for slow body modes in cylindrical flux tubes with the
model prediction obtained by imposing the continuity of the radial component of
the velocity and total pressure at the boundary of the flux tube. Our results
show that, to a high accuracy (less than 1\% for the considered model), the
conditions of continuity of the component of transversal velocity and pressure
at the boundary can be neglected when modelling slow body modes under
photospheric conditions.
