  Magnetohydrodynamic waves are important for diagnosing the physical
parameters of coronal plasmas. Field-aligned flows appear frequently in coronal
loops.We examine the effects of transverse density and plasma flow structuring
on standing sausage modes trapped in coronal loops, and examine their
observational implications. We model coronal loops as straight cold cylinders
with plasma flow embedded in a static corona. An eigen-value problem governing
propagating sausage waves is formulated, its solutions used to construct
standing modes. Two transverse profiles are distinguished, one being the
generalized Epstein distribution (profile E) and the other (N) proposed
recently in Nakariakov et al.(2012). A parameter study is performed on the
dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius
ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters
($\rho_0/\rho_\infty$ and profile steepness $p$) and flow parameters (magnitude
$U_0$ and profile steepness $u$). For either profile, introducing a flow
reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends
sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By
far the most important effect a flow introduces is to reduce the capability for
loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be
substantially reduced in the case with flow relative to the static one. If the
density distribution can be described by profile N, then measuring the sausage
mode period can help deduce the density profile steepness. However, this
practice is not feasible if profile E better describes the density
distribution. Furthermore, even field-aligned flows with magnitudes
substantially smaller than the ambient Alfv\'en speed can make coronal loops
considerably less likely to support trapped standing sausage modes.
