PSGen is a new general purpose Fortran program which has been written to facilitate the Monte Carlo phase space integration of the S matrix element of any 2 -> n scattering process, with n=2,...,9, provided by the user.The program is written in Fortran 90/95 . It utilizes a new very fast algorithm that automatically generates calls to ready made Fortran subroutines containing different phase space parameterizations of the considered class of processes. The parameterizations take into account mappings of poles due to the Feynman propagators of unstable heavy particles decaying into 2 or 3 on shell final state particles according to predefined patterns, possible single or double t-channel poles and peaks due to one on shell photon or gluon radiation. The individual subroutines are organized in a single multichannel kinematical subroutine which can be easily called while computing the phase space integral of the S matrix element as a function of generated particle four momenta, in either the leading or higher orders of the perturbation series. The particle four momenta can be used in a quadruple precision version, if necessary.