Here, a multi-physics approach is presented for the design optimisation of an integrated modular motor drive (IMMD). The system is composed of a modular permanent magnet synchronous motor (PMSM) and a GaN-based modular motor drive power stage. The multi-physics model includes motor drive inverters and DC-link capacitor bank (electrical model), stator windings and rotor magnets (electromagnetic model), heat sink (thermal model), and a geometrical model. The main purpose of the design optimisation is to obtain the highest power density possible, which is quite critical in integrated drives. Due to the integrated structure, the system has several interdependencies and parameters are selected based on those relationships. An 8kW IMMD system design is proposed from the developed optimisation tool and evaluated. The resultant system has a power density of 0.71kW/lt, drive efficiency of 98.3%, and motor efficiency of 96.6%.