A simplified analysis of static instability in supercritical parallel channel systems is presented for the sake of deriving insights into the phenomenon and understanding better the parameters that affect the phenomenon. The oscillatory, density-wave type of instability received more attention in reported works; hence, that is not the main focus here. An improved set of non-dimensional parameters for general supercritical flow dynamics is proposed. They were obtained by modifying Ambrosini’s parameters using a different definition of the pseudo-critical point, obtained from insights gleaned from previous analyses. These new parameters show much less scatter in the ‘normalized density versus normalized enthalpy’ plot than the original parameters. This development would be of value to engineers working on supercritical flow designs. In general, static instability is encountered in low inlet temperatures and would likely be a possibility during start-up of a reactor rather than during normal operation. However, flow orientation does have a bearing on its occurrence, as vertical down-flow shows a greater proclivity to static instability than up-flow.