Two-dimensional (2D) transition-metal dichalcogenides (TMDs) monolayers have found various applications spanning from electronics in physics to catalysis in chemistry due to their unique physical and chemical properties. Here, the effect of structure engineering on the physical and chemical properties of transitionmetal disulfide monolayers (MS2) is systematically investigated based on density functional theory (DFT) calculations. The calculation results show that waved MS2 (w-MS2) can be achieved under compression due to the zero in-plane stiffness, leading to high flexibility within a wide range of compression. The bandgap and conductivity of semiconducting w-MS2 are reduced because the d orbitals of transition-metal elements become more localized as the curvature increases. A transition from a direct band to an indirect one is observed in w-MoS2 and wWS2 after a critical strain. We further demonstrate the structure engineering can modulate the magnetism of w-VS2, leading to nonuniform distribution of magnetic moments along the curvature. Furthermore, we find that waved TMDs show reduced Gibbs free energy for hydrogen adsorption, resulting in enhanced catalytic performance in hydrogen reaction evolution (HER). It is expected that the waved 2D TMDs may find applications into various areas, such as nanodevices and catalysis.