Minimum energy structures of short (3,3) single wall carbon nanotube (SWCNT)–polyethylene (PE) structures, as well as the binding energy between the SWCNT and PE, were obtained from three commonly used molecular mechanics force fields and first principles methods. The molecular force fields were the Dreiding, Universal and Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force fields and the first principles methods included the B3LYP density functional and MP2 post-Hartree Fock methods with, typically, 6-311G, 6-311G(d,p) and 6-311G(2d,2p) basis sets. These calculations show that the results obtained from all force fields are in qualitative agreement with the first principles results, and that PE prefers to be aligned with a non-zero angle along the SWCNT axis, where the angle depends on the force field or first principles method used. This indicates that longer PE chains may wrap around SWCNTs. This was studied using the COMPASS force field with longer (5,5) SWCNTs interacting with a PE chain and, in agreement with the minimum energy calculations, the PE wrapped around the SWCNT thereby increasing the radius of gyration of the PE. This force field was also used to assess the effect of (5,5) SWCNTs on the mechanical properties of PE nanocomposites. The calculated interfacial shear stress and interfacial bonding energy of SWCNT–PE structures was 141.09 MPa and 0.14 N/m. The simulations show that using short SWCNTs as reinforcement does not increase the Young’s modulus for the systems studied here, whereas longer, aligned SWCNTs increased the Young’s modulus in the SWCNT axial direction.