We present a simple new technique to simulate the elongational flow of a simple atomic fluid by nonequilibrium molecular dynamics (NEMD). This technique involves simulating elongational flow by applying a frequency-dependent strain rate that ensures that the system attains a temporally periodic steady state. For a given magnitude of the strain rate, quantities of interest, such as the diagonal elements of the pressure tensor, and hence elongational viscosities, are then calculated by extrapolating their frequency-dependent values down to zero frequency. The zero frequency results are in excellent agreement with independent conventional NEMD calculations of these quantities. The main advantage of this technique is that it provides a convenient and consistent means of extrapolating to the zero-frequency (steady elongation) elongational viscosity, unlike the standard method, in which it may be difficult to distinguish between the transient response and the steady-state response.