The design of the best structure for a given purpose depends upon the criterion used for optimisation. Structures may be designed to safely transmit a given system of forces using the least weight of material.. They may also be designed to have maximum stiffness of a certain type for a given weight or alternatively to have the greatest possible fundamental frequency of vibration. These problems, although in general distinct from one another, are closely related and much can be achieved towards maximisation of stiffness and frequency by the use of minimum weight designs. In fact it can be shown that a minimum weight framework is the stiffest structure of that weight for the force system, which it is designed to carry.x The present report is concerned exclusively with the problem of the design of structures of minimum weight, which are required to transmit specified forces. Some attention will be given to frameworks because, in particular, methods of approximate numerical analysis are more readily formulated for this type of structure, but the main emphasis will be placed upon the design of structures formed from plates of variable thickness reinforced by direct load carrying members. See para,l.4