AbstractMonolayers of transition metal dichalcogenides can exist in several structural polymorphs, including 2H, 1T and 1T′. The low-symmetry 1T′ phase has three orientation variants, resulting from the three equivalent directions of Peierls distortion in the parental 1T phase. Using first-principles calculations, we predict that mechanical strain can switch the relative thermodynamic stability between the orientation variants of the 1T′ phase. We find that such strain-induced variant switching only requires a few percent elastic strain, which is eminently achievable experimentally with transition metal dichalcogenide monolayers. Calculations indicate that the transformation barrier associated with such variant switching is small (<0.2 eV per chemical formula unit), suggesting that strain-induced variant switching can happen under laboratory conditions. Monolayers of transition metal dichalcogenides with 1T′ structure therefore have the potential to be ferroelastic and shape memory materials with interesting domain physics.