In this paper, the stress-induced phase transitions in a shape memory alloy (SMA) tube under torsion and pre-twisted tension are studied analytically. A constitutive model with the specific forms of Helmholtz free energy and mechanical dissipation rate is employed to formulate the governing system. Exact solution of the tube under pure torsion is first derived and the shear stress-shear strain response is determined, which reveals the hardening effect. For the pre-twisted tube under uniaxial tension, the one-dimensional asymptotic tensile stress-tensile strain relations for the austenite, the phase transition and the martensite regions are derived by using the asymptotic expansion method. By properly defining an elastic energy potential, the present system can be viewed as an elastic problem, which can be related to the problem of Ericksen's bar. The analytical formulas for the nucleation and propagation stresses in terms of the pre-shear strain (caused by the pre-twist) are obtained. Tension tests with fixed pre-twists on SMA thin-walled tube are conducted, with a focus on the stress-strain response. The measured values and the analytical formula for the propagation stress are used to determine the material parameters, which, in turn, yields the up-down-up response of a shape memory alloy tube under pure tension. The tendency and turning point of the phase transformation in the pre-twisted tube from localization to homogeneous deformation are also determined, which suggests a plausible way to avoid the instability in actuation applications. © 2016 Elsevier Ltd . All rights reserved.