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Near-equiatomic NiTi is known to exhibit multiple martensitic allotropes, including B19′, B19″ and base-centred orthorhombic (BCO). Formation of these martensites is associated with volume expansions, thus hydrostatic loading has direct influence on the stability, ground-state, transformation pathways and the structures of these phases. This work was conducted to clarify some uncertainties in the literature concerning the effect of hydrostatic tension on these properties of the martensite allotropes using the generalised solid-state nudge elastic band method implemented in density functional theory. It was found that higher hydrostatic compression favours phases of lower specific volumes, and higher hydrostatic tension favours phases of higher specific volumes. B19′ is stable at above 2 GPa compression, B19″ is stable within -6 GPa tension and 6.6 GPa compression and BCO is stable between -8 GPa tension and 8.8 GPa compression.