This work is a theoretical study of 40-atom Pt-Au clusters which are of interest owing to the electronic shell closure of 40-atom noble metal clusters and the current focus on bimetallic Pt-Au clusters as catalysts. The methodology is a complementary combination of a genetic algorithm search for an empirical potential and density functional theory (DFT) reoptimization. Structures based on truncated-octahedral, icosahedral, decahedral and fivefold pancake geometries are found to be energetically favoured for different composition regions at the empirical-potential level and this is partially confirmed at the DFT level. The large HOMO-LUMO gaps found for the icosahedral and fivefold pancake structures indicate electronic shell closure effects, while the truncated-octahedral and decahedral structures have small gaps. The DFT calculations confirm that, for Pt 20 Au 20 truncated-octahedral structures, the Pt core Au shell configuration which has two Au atoms capping the (100) facets is most energetically favoured, and the layered (phase segregated) configuration also has lower energy compared with the Au core Pt shell and mixed configurations.