Abstract: In structural design we usually use a well-known criterion,σ≤σ.However, the maximum stress only covers a very small region in the structure and this region does not always coincide with the weakest point of the material used.The strength characteristics of the advanced composites are the linear elasticity and the large scatter band of strength so that the conventional criterion does not meet the design requirements very well. From the statistical point of veiw this problem is discussed and treated in this paper, which includes four aspects:the scatter band of strength,series model,parallel model and some simple structural applications.