This Ph.D. dissertation presents a multifaceted study of the instability-induced pattern transformations in soft particulate composites undergoing large deformations, via various numerical approaches and considering different forms and dimensions of the composite configurations. This study also emphasizes the whole process study of the instability phenomenon in composite materials, from prior- to post-buckling regimes.Specifically, results are presented for different forms of particulate composites, including 1) 2D rectangular cells with a single-sized inclusion, 2) 2D rectangular cells with two different-sized inclusions, and 3) 3D cuboid cells with a single-sized sphere inclusion. Numerical results derived from various methods are shown and discussed, including those from i) Bloch-Floquet analysis, ii) Post-Buckling analysis, iii) Energy quasi-convexification analysis, and iv) a hybrid method that implements Bloch-Floquet analysis in the post-buckling regime. In addition to presenting the dependence of instability critical characteristics on the composite’s initial geometric configurations, the study also highlights key findings and novel insights, including i) the transition of buckling behavior as the composite’s manifestation of two soft particulate systems; ii) the divergence of linearized instability predictions in their post-buckling regimes; iii) the unique “seemingly non-periodic” state of buckling modes; iv) the occurrence of secondary instability in the post-buckling regime of the particulate composite; v) the interplay of two different-sized inclusions in particulate composites; and vi) the differences in instability behaviors between 2D and 3D particulate composites. Additionally, a post-processing method based on the discrete Fourier transformation (DFT) is developed for characterizing post-buckling development. This method enables accurate identification of critical characteristics compared to traditional visual inspection of repeating blocks. It also facilitates the future application of experimental identification of instability-induced pattern transformations by circumventing test defects.