A general algorithm for the construction of infinite periodic minimal surfaces (IPMS) via their Weierstrass function is outlined, enabling parameterisation of known examples, and forming the bases of a systematic search for all such surfaces. For the 'regular' class of IPMS (including the low genus surfaces) the Weierstrass function has a simple form, permitting a complete listing of all possibilities. The method is then readily extended to parametrisation of the 'irregular' class of IPMS, and its generally illustrated with several previously unsolved examples.