Mo- and W-dichalcogenide compounds have a two-dimensional monolayer form that differs from graphene in an important respect: it can potentially have more than one crystal structure. Some of these monolayers exhibit tantalizing hints of a poorly understood structural metal-to-insulator transition with the possibility of long metastable lifetimes. If controllable, such a transition could bring an exciting new application space to monolayer materials beyond graphene. Here we discover that mechanical deformations provide a route to switching thermodynamic stability between a semiconducting and a metallic crystal structure in these monolayer materials. Based on state-of-the-art density functional and hybrid Hartree-Fock/density functional calculations including vibrational energy corrections, we discover that MoTe2 is an excellent candidate phase change material. We identify a range from 0.3 to 3% for the tensile strains required to transform MoTe2 under uniaxial conditions at room temperature. The potential for mechanical phase transitions is predicted for all six studied compounds.