The nanostructure of biological materials is built with hard mineral crystals embedded in soft protein matrix in a staggered manner. The staggered arrangement of the crystals is assumed to be critically important for the stability of the nanostructure. But the mechanism is not fully understood. In this paper, a mechanical model, considering the effects of overlapping ratio between the crystals, i.e., the staggering position, is developed for analyzing the buckling behaviors of the nanostructure. It is found that the buckling strength increases with the overlapping ratio λ in the range of 0–1/2 and reaches a peak value at λ = 1/2 that is generally adopted by nature's design of the biological materials. The effect of aspect ratio and volume fraction of mineral crystals are further analyzed at various overlapping ratios, and the results are in general consistent with previous studies for the case of λ = 1/2. In addition, the lower and upper limits of the buckling strength are obtained. Finally, we show that the contact between mineral tips can significantly enhance the buckling strength of the nanostructure when the aspect ratio of minerals is small.