The fundamental problem of structural design is the determination of structures of minimum weight which safely equilibrate a given system of external forces. The classical theorem of Michell gave basic requirements for such a structure. The first part of this paper analyses the geometrical layout of two-dimensional structures which satisfy these requirements, making use of the analogy with the theory of plane plastic flow. Expressions for the calculation of sizes and the total volume of the structural members are developed. Method of graphical construction of the structural layout is also given.