We investigate simple gravitational lens models for the recently disco
vered quadruple QSO B 1422+23 1. The image configuration in this multi
ple QSO system indicates that the gravitational deflector has a consid
erable ellipticity; we therefore explore lensing models based on ellip
tical mass distributions. Employing a simple fitting procedure, we sho
w that (1) our models cannot satisfactorily account for the details of
the image configuration, in particular, the flux ratios are difficult
to reproduce; (2) Our best model is a combination of an elliptical de
flector and externally applied shear; the direction of the shear is in
accordance with the position of two galaxies detected near the QSO im
ages, and may well be produced by them. If this interpretation is corr
ect, our best model is in fact quite similar to the model of Hogg & Bl
andford, except that we account for the ellipticity of the main deflec
tor, which reduces the mass of the nearby galaxies to produce the nece
ssary shear. The fact that the models do not improve if the position o
f the lens center is allowed to vary from its observed position is a s
trong argument in favour of it being indeed the main lensing galaxy.