Because of their simplicity, axisymmetric mass distributions are often used to model gravitational lenses. Since galaxies are usually observed to have elliptical light distributions, mass distributions with elliptical density contours offer more general and realistic lens models. They are difficult to use, however, since previous studies have shown that the deflection angle (and magnification) in this case can only be obtained by rather expensive numerical integrations. We present a family of lens models for which the deflection can be calculated to high relative accuracy (10-5) with a greatly reduced numerical effort, for small and large ellipticity alike. This makes it easier to use these distributions for modeling individual lenses as well as for applications requiring larger computing times, such as statistical lensing studies. FASTELL is a code to calculate quickly and accurately the lensing deflection and magnification matrix for the softened power-law elliptical mass distribution (SPEMD) lens galaxy model. The SPEMD consists of a softened power-law radial distribution with elliptical isodensity contours.