We present simple changes to the cell method for neighbor list construction that enable it to be used in molecular dynamics studies of systems subject to a planar elongational flow field. The modifications for planar elongational flow are similar to those required for planar shear flow and should be easy to incorporate into any cell neighbor list method that is used in simulations of homogeneous shear. The execution time of the code at equilibrium is shown to be proportional to the number of particles N. The introduction of the modifications allowing shear, and more importantly, elongational flow are shown to affect the performance of the code in both CPU time and memory usage. The modifications to enable the simulation of planar elongational flow using the cell method of neighbor list construction will not introduce any higher order dependency if applied to code that is N-dependent in planar shear flow. We use this code to study large systems of diatomic molecules at low strain-rates, and find that the linear regime in planar elongational flow can be determined by the ratio of the two planar elongational viscosity functions. The properties investigated in planar shear flow, such as angular velocity and alignment angle, were inconsistent with the shear viscosity results in their evaluation of where the linear regime ends. The high precision of the results allowed us to accurately determine the coefficients in the retarded-motion expansion.