Summary: In this paper, we investigate the elliptical instability exhibited by two counter-rotating trailing vortices. This type of instability can be viewed as a resonance between two normal modes of a vortex and an external strain field. Recent numerical investigations have extended earlier results that ignored axial flow to include models with a simple wake-like axial flow such as the similarity solution found by G. K. Batchelor [J. Fluid Mech. 20, 645–658 (1964; Zbl 0151.40401)]. We present herein growth rates of elliptical instability for a family of velocity profiles found by D. W. Moore and P. G. Saffman [Proc. R. Soc. Lond., Ser. A 333, 491–508 (1973; Zbl 0263.76015)]. These profiles have a parameter \(n\) that depends on the wing loading. As a result, unlike the Batchelor vortex, they are capable of modelling both the jet-like and the wake-like axial flow present in a trailing vortex at short and intermediate distances behind a wingtip. Direct numerical simulations of the linearized Navier-Stokes equations are performed using an efficient spectral method in cylindrical coordinates developed by T. Matsushima and P. S. Marcus [J. Comput. Phys. 137, No. 2, 321–345 (1997; Zbl 0887.65103)]. We compare our results with those for the Batchelor vortex, whose velocity profiles are closely approximated as the wing loading parameter \(n\) approaches 1. An important conclusion of our investigation is that the stability characteristics vary considerably with \(n\) and \(W_{0}\), a parameter measuring the strength of the mean axial velocity component. In the case of an elliptically loaded wing (\(n=0.50\)), we find that the instability growth rates are up to 50 % greater than those for the Batchelor vortex. Our results demonstrate the significant effect of the distribution and intensity of the axial flow on the elliptical instability of a trailing vortex.