Dependence on density contrast ρ₀/ρ_∞ of threshold length-to-radius ratio (L/a)_cutoff below which standing sausage modes are trapped. Both a) profile E and b) profile N are examined. The solid black curves are for the static case, while the colored curves represent the non-static cases with the flow magnitude U₀ ranging from 0.02 v_A∞ to 0.08 v_A∞. In the computations, both the density and flow profile steepness, p and u, are taken to be 2. The dashed straight lines in both panels represent the threshold length-to-radius ratio analytically derived in the static case for a step-function profile (Eq. (4)). Furthermore, the hatched area corresponds to the parameter range for typical active region (AR) loops. The horizontal dashed line represents the length-to-radius ratio of the flaring loop reported in Nakariakov et al. (2003).