A general approach to optimal structural design is proposed. Rather than optimizing a single quantity for a structure, the aim is to present an optimal design method which incorporates most or all of the properties of a structure within a given mathematical model. There are three justifications for the use of the word ‘natural.’ Within the static, purely mechanical theory of continua there are two numbers which may be ‘naturally’ associated with the deformed state of a structure: its mass and its stored energy. This association provides the criteria for the comparison of various designs. The ‘natural’ extension of maximization and minimization of a single criterion appears to be the concept of Pareto-optimality in multicriteria decision making. Thus, a natural structural shape is one which results from the calculation of Pareto-optimal decisions for the criteria mass and stored energy. Generally, this procedure yields a one-parameter family of natural shapes; a particular member of the family is obtained with the subsequent specification of any additional constraint. Finally, some of the resultant designs are compared with presumably optimal structures in ‘nature.’ The emphasis here is on the presentation of examples; the results indicate that the specification of the general properties of this class of structures would be of interest.