  We develop a semi - analytical method to reconstruct the lensing potential in
quadruply imaged gravitational lens systems. Assuming that the potential
belongs to a broad class of boxy non - elliptical models, we show how it is
possible to write down a system of equations which can be numerically solved to
recover the potential parameters directly from image positions and using
physical constraints. We also describe a code developed to search for solutions
of the system previously found and test it on simulated cases. Finally, we
apply the method to the quadruple lens PG1115+080 which allows us to get also
an estimate of the Hubble constant H_0 from the measured time delay as H_0 =
56_{-11}^{+17} km/s/Mpc.
