Ti50Ni50-xCux alloys are observed to exhibit multiple martensitic transformations from B2 to an orthorhombic B19 and a monoclinic B19′ phase. In addition, DFT calculations have predicted a B19ʺ phase with a higher monoclinic angle as the thermodynamically stable ground state. This study investigated the effects of Cu content and shear stress on the monoclinic angles, phase stabilities of the various martensites, the minimum energy pathways, and the relative total energies among the phases in this pseudo-equiatomic Ti(Ni50-xCux) system. A new monoclinic phase (B19M) with a monoclinic angle lower than that of B19′ was found at above a critical Cu content. This confirms the formation of an intermediate phase in the martensitic transformation sequence of the pseudo-equiatomic Ti(Ni50-xCux) system but contradicts the crystal structure of the experimentally observed phase. It was found that the monoclinic angles of both B19M and B19ʺ decrease with increasing the magnitude of an opposing shear stress to their monoclinic distortion. At above certain critical values of the opposing shear stress, the B19M and B19ʺ phases destabilise and transform to lower monoclinic angle phases. In addition, the evidence suggests that the experimentally observed monoclinic B19′ phase is in fact a distorted B19ʺ with a reduced monoclinic angle under an opposing shear stress. With the same argument, the experimentally reported B19 phase is a metastable phase formed under the effect of an opposing shear stress to the monoclinic distortion of B19M.