In this paper molecular dynamic simulation is used to examine the mechanical properties of multilayer molybdenum disulfide (MoS2) and graphene/MoS2 heterostructure under uniaxial tensile and normal compressive strain. The effects of temperature, layer number and stacking order of layers on the stress-strain curve and elastic properties are studied. We find that the Young's modulus and vertical elastic constant of the heterostructure are much larger than that of MoS2 which is due to the higher stiffness and Young's modulus of graphene compared to MoS2. Furthermore, the results reveal that graphene/MoS2 heterostructure is more resistant to the variation of temperature. While the rise in temperature results in the decrease of elastic constants, fracture strain and fracture stress of both structures, the increase in the number of layers only affects the elastic properties of heterostructure and has little influence on the stiffness of multilayer MoS2. Our simulations also illustrate that the highest energy stacking orders, AA(3) and AB(3), wherein S atoms of top layer are located above the S atoms of bottom layer, have the lowest elastic constants among all structures. (C) 2017 Elsevier B.V. All rights reserved.