Abstract: Numerical simulationis an effective tool in studying nano-materials with tinycharacteristic length, and may be the only option when thegeometry size of these materials is down to the nano-scale and noexperimental testing system is available. This paper reviewsrecent advances in molecular dynamics simulations andfirst-principles calculations on mechanical behaviors ofnano-materials, with focuses laid on lattice instability, idealstrength, interfacial fracture, mechanical and electric propertiesof carbon nano-tubes and ferroelectric nano-materials. It isexpected that the presentation of these research efforts coulddemonstrate some of practical computational strategies andmethodologies in conducting atomistic simulations of mechanicalproperties of tiny materials. Some problems in need of furtherstudies are identified as well.