Axial flux machines offer an inherent torque density advantage over conventional radial flux machines and are increasingly being considered for transportation electrification applications. Electrification of off-highway vehicles is notoriously challenging due to extreme power density requirements. This paper investigates the use of axial flux machines for off-highway vehicle electrification. To maximize the power density, a hydraulic pump is integrated with the axial flux machine, resulting in a single modular, electric/hydraulic machine. This paper first compares three popular axial flux machine variants using an FEA-based design optimization approach. The single rotor, single stator variant is identified to be the most promising for integration with the hydraulic pump. Next, a multi-physics framework of the complete integrated hydraulic pump and axial flux machine is developed to search the design space. The results indicate promising potential for this concept to realize efficiency over 85% and power density over 5kW/kg for the complete machine (electric machine, hydraulic pump, and thermal management system), while utilizing conventional materials (thin gauge silicon steel, N45 magnets, and magnet wire).