Engine cooling systems contain multiple parallel flow paths, which under sub-cooled boiling conditions can experience excursive flow instability. This study presents an analytical model describing the pressure drop in a channel subjected to flow boiling. Using water as the working fluid, results are presented showing the effect of inlet velocity and surface heat flux on the overall pressure drop. The accuracy of this model for water has been verified. The calculations show that for typical engine operating conditions, the cooling passage can contain regions of partially developed and fully developed sub-cooled boiling.