Abstract: Structure designers are concerned about whether the statically determinate or indeterminate structure is lighter.Therefore,three theorems for weight characteristics of statically determinate and indeterminate structures are presented and proved,and the essentials of the problem are explained in this paper.Due to the limited space on printed pages only one example,i.e.the optimization of a 10-bar plane truss is given.It is a rather difficult task and usually requires more than 10 iterations;even so,its solution is not good enough.But it is calculated only by two iterations in this paper,and its solution is quite well.In general,for other examples suitable to the above mentioned theorems,it is possible to obtain a satisfactory solution only through one or two iterations.