Nacre, bone, spider silk, and antlers are some examples of biological composites that exhibit a great combination of mechanical properties such as high strength, stiffness, and toughness when compared to that of their constituents using which they are made up of. This has inspired many researchers to investigate bio-inspired composites to explore the possibilities of making synthetic composites with superior mechanical properties using relatively weaker constituents. There are many reasons behind the achievement of a biological composite’s superior mechanical properties, which range from the selection of constituents to its final arrangement. The basic structure of the above-mentioned biological composites is a kind of brick-and-mortar structure in which platelets with a defined configuration are dispersed in a pool of matrix. Here, the parameters significantly influencing the final mechanical properties are Young’s moduli ratio of platelet to the matrix, the platelet aspect ratio, and the arrangement of platelets, especially the hierarchy. The present study focuses on two staggering types found in nature, regular and stairwise, and conducts a failure analysis on one-hierarchical composites with these configurations. The inclusion of the first failure in the analysis is found to contribute to composite toughness significantly. Case studies using industry materials and recent research works support these findings. Analytical models are formulated for predicting the properties of non-self-similar two hierarchical composites, demonstrating good agreement with finite element analysis results. The generalized model aids in simplifying the design process, providing initial estimations of mechanical properties for hierarchical composites before full-scale fabrication and offering practical insights for future material design.