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With increasing interest in the use of glassy carbon (GC) for a wide variety of application areas, the need for developing fundamental understanding of its mechanical properties has come to the forefront. Further, recent theoretical and modeling works that shed some light on the synthesis of GC through the process of pyrolysis of polymer precursors have highlighted the possibilities of a revisit to investigation of its mechanical properties at a fundamental level. While there are isolated reports on the experimental determination of its elastic modulus, insights into stress-strain behavior of GC material under tension and compression obtained through simulation, either at molecular level or for the bulk material is missing. This current study fills the gap at the molecular level and investigates the mechanical properties of GC using molecular dynamics (MD) simulations which model the atomistic level formation and breaking of bonds using bond-order based reactive force field formulations. The molecular model considered for this simulation has a characteristics 3D cagey structure of 5-, 6-, and 7-membered carbon rings and graphitic domain of a flat graphene-like structure. The GC molecular model was subjected to loading under varying strain rates (0.4/ns, 0.6/ns, 1.25/ns, and 2.5/ns) and varying temperatures (300 - 800 K) in each of the three axes x, y, and z. The simulation showed that GC molecule has distinct stress-strain curves under tension and compression. In tension, MD modeling predicted mean elastic modulus of 5.71 GPa for a single GC molecule with some dependency on strain rates and temperature, while in compression, the elastic modulus was also found to depend on the strain rates as well as temperature and was predicted to have a mean value of 35 GPa