Molybdenum disulfide (MoS2) is a promising layer-structured material for use in many applications due to its tunable structural and electronic properties in terms of its structural phases. Its performance including efficiency and durability is often dependent on its mechanical properties. To understand the effects of the structural phase on its mechanical properties, a comparative study on the mechanical properties of bulk 2H, 3R, 1T, and 1T′ MoS2 was conducted using the first-principles density functional theory. Since considerable applications of MoS2 are developed through strain engineering, the impact of the external pressure on its mechanical properties was also considered. Our results suggest a strong relationship between the mechanical properties of MoS2 and the structural symmetry of its crystal. Accordingly, the impacts of the external pressure on the mechanical properties of MoS2 also greatly vary with respect to the structural phases. Among all of the considered phases, the 2H and 3R MoS2 have a larger bulk modulus, Young’s modulus, shear modulus, and microhardness due to their higher stability. Conversely, 1T and 1T′ MoS2 are less strong. As such, 1T and 1T′ MoS2 can be a better candidate for strain engineering.