Using a parametric representation, it was proved in 1959l that the static and kinematic approaches to the plastic collapse problem are dual linear programming problems. In this paper, the generalized parameters used previously are given physical meaning and shown to be readily programmed for computer application. One important advantage of the method is that the equations can be written in general terms such that no assumptions regarding the structural form need to be built into the program. The application is extended to the more general problem of automatic plastic design and it is shown that the inclusion of a serviceability constraint (e.g. no plastic hinges at a given load factor) is trivial in this formulation. The difficult problem of several loading cases is shown to be readily treated by designing for a given load factor for shakedown rather than plastic collapse.Though this latter facility, by its dependence on elastic behaviour, requires iteration of the stiffness of the structure, rapid convergence appears to be generally obtained. Finally a method is suggested whereby an adequate allowance for frame instability may be made without destroying the linearity of the equations. Though the equations, as developed, have application to steel framed structures in mind, the extension to the limit design of reinforced concrete structures appears to present no additional complications. @ 1972 by John Wiley & Sons, Ltd.