Gear pumps are largely employed in aero-engine fuel systems to provide the combustor with fuel at adequate pressure and flow rate. The radial load applied on the gears, as a consequence of the pump pressure rise, is entirely supported by the hybrid journal bearings. Lubrication of these is accomplished using low viscosity aviation fuel, which makes the design and analysis of journal bearings particularly challenging. A numerical model has been developed to support the analysis and future design of hybrid journal bearings for fuel pump applications. The primary objective of the tool is to characterise the equilibrium position of the journal during steady-state operation at part and full load, where the resultant elastic displacements are more significantly affecting the pressure distribution of the lubrication film. The developed method effectively combines Elrod's cavitation algorithm with the dimensionless pressure definition known as the Vogelpohl parameter, resulting in a simple and robust methodology to characterise the pressure distribution within the lubricant for different bearing designs and operating conditions. Six different multidimensional root-finding solvers have been implemented and their performance evaluated against robustness, accuracy and computational speed requirements. Newton-Raphson based methods have shown promising trade-offs for the problem at hand. Validation of the tool has been made comparing experimental film thickness measurements, performed on a fuel pump from a modern turbofan engine, with predicted data from the numerical model.