Dual phase HCP(α)-BCC(β) alloys such as aerospace alloy Ti-6Al-4V and nuclear alloy Zr- 2.5Nb require hot deformation during thermo-mechanical processing to achieve near-net shape. During hot deformation, the development of strong crystallographic texture leads to highly anisotropic material properties, due to the low symmetry of the HCP phase, which makes up the majority of the material when it is cooled to room temperature. Processing at temperatures close to 1000 degrees celsius in the case of dual-phase titanium alloys involves the co-deformation of both phases, but the details of this process are obscured by phase transformation on cooling, making it difficult to fully understand how texture develops in both phases before cooling. Using full-field crystal plasticity modelling, it is possible to assess the effect of the HCP α-phase grain morphology on the texture evolution of both phases at hot-working temperatures. These predictions can be compared against experimental measurements of texture to explain how the shape, orientation, and local neighbourhood affects texture development during hot-working. In this work, we have used the DAMASK modelling framework to simulate the deformation of synthetic dual-phase microstructures with different grain shapes and different orientations, which are representative of the range of microstructures thought to exist at processing temperatures. It is shown that the shape of the α grains significantly affects the degree of strain localisation, in the form of shear bands, that develop in the continuous β phase. This effect is particularly important when the α grains are in a hard orientation, i.e. poorly aligned for easy slip. This shearing of the β matrix can also contribute to the development of the texture of the α, even when deformation in the α phase itself is limited. These results help to explain the development of the characteristic texture components in the α phase at elevated temperatures, and also the development of strong microtextures during the hot working of these materials.