The most stable ultrathin molybdenum disulfide (MoS2) nanowires of different cross-section radii were predicted by the simulated annealing basin-hopping (SABH) method with the Tersoff potential. Before the SABH procedure, the Tersoff potential parameters for MoS2 were fitted by the force matching method (FMM) on the basis of bulk Mo, S, and MoS2 material properties. Combined with the SABH method, a penalty function was imposed in the radial dimension of the nanowire to constrain all atoms to evolve along the designated axial direction of MoS2 nanowires. By molecular dynamics (MD) simulation of uniaxial tension, the mechanical properties including the Young’s moduli, yielding stresses, and strengths of these MoS2 nanowires were determined. In order to understand the feasibility of MoS2 nanowire application on nano-devices, the thermal stability of these ultrathin MoS2 nanowires was also investigated by the temperature elevation process by the MD simulation.