In this paper, the linear elastic response to uniaxial tension of amorphous polyethylene was investigated by using Molecular Dynamics (MD) simulation. The polymeric system was initiated using a Monte Carlo-based technique and then equilibrated by a relaxation sequence at temperature of 100 K under a NPT control. Uniaxial tension test was carried out by modifying the corresponding component of the pressure tensor, with a loading rate of 0.5 bar/ps. The results showed that at 100 K (which is smaller than the glass transition temperature), the amorphous polymeric material exhibited a linear elastic response to uniaxial tension. The obtained Young’s modulus and Poisson’s ratio were also compared with values reported in the literature. Finally, parametric studies were performed on the stress-strain curve as a function of loading axis, number of chains and number of monomer units, respectively.