The extent to which the intrinsic mechanical properties of polymer fibers depend on physical size has been a matter of dispute that is relevant to most nanofiber applications. Here, we report the elastic and plastic properties determined from molecular dynamics simulations of amorphous, glassy polymer nanofibers with diameter ranging from 3.7 to 17.7 nm. We find that, for a given temperature, the Young's elastic modulus E decreases with fiber radius and can be as much as 52% lower than that of the corresponding bulk material. Poisson's ratio ν of the polymer comprising these nanofibers was found to decrease from a value of 0.3 to 0.1 with decreasing fiber radius. Our findings also indicate that a small but finite stress exists on the simulated nanofibers prior to elongation, attributable to surface tension. When strained uniaxially up to a tensile strain of ε = 0.2 over the range of strain rates and temperatures considered, the nanofibers exhibit a yield stress σ y between 40 and 72 MPa, which is not strongly dependent on fiber radius; this yield stress is approximately half that of the same polyethylene simulated in the amorphous bulk.