Prediction of the quench evolution is an important task in designing superconducting magnets. Especially when different coils are coupled together, with possibility of energy exchange among them, very dangerous situation may happen, not easy to predict with simple analytical evaluation. The code QLASA described in this report is originated from the codes DYNQUE and QLASA in use at the superconducting magnet group of the LASA laboratory (University and INFN-Milan): it is mainly intended for adiabatic multiple solenoids, with different power supplies, but can now deal partially with different geometries. It can be used as a design tool, since it allows to control many parameters, it treats the windings as a medium of average properties (that may differ along the three dimensions) and it is coupled with an extensive custom library of cryogenic properties, although its main use has been restricted so far to NbTi and Nb3Sn conductors. It is particularly useful when internal voltages and internal temperatures need to be computed. The report describes the winding modeling, all steps of thermal and electrical computations and how they are separated as well as the coupling with the cryogenic library. The limitations of the codes, written in F77, are explained and underlined, as well as the suggestion to use it in geometry different from the axis-symmetric. Finally a few examples of input files are given and comparisons among predictions and experiments are reported.