Fine-fragments (or fines) are an unavoidable result of rock blasting and the subsequent comminution process. They are often less valuable than larger fragments or even unsellable and hence have economic and environmental impacts. Thus, understanding the source mechanisms forming the fines has high industrial and research interest. Two mechanisms are responsible for the creation of the fines: compressive crushing-shearing and branching-merging of tensile cracks. In this work the focus is put on numerical modeling of blast-induced fragmentation and its mathematical formulation in order to investigate the role of branching-merging in blasting fragmentation and fines generation. In the first part, two numerical methods, i.e. finite element method (FEM), Abaqus/Explicit, and discrete element method, HiDEM code, are used for simulating quasi-brittle material response to civil blast loads. The dynamic crack propagation, branching-merging and the resultant mass passing fraction (MPF) in lab-scale cylindrical specimens are analyzed. The 2D FEM simulations produce reasonable post-mortem end-face fracture patterns, while the HiDEM simulations produce 3D crack networks and MPF curves similar to experimental results. The second part deals with 3D HiDEM modeling of lab-scale cylinders of magnetite mortar (Ø140 mm × 280 mm). The computed Fragment Size Distributions (FSDs) in an s-n(s) description of fragmentation are compared with those of the experiments which are confined by a cylindrical layer of pre-stressed aggregate. An FSD function with three terms is proposed. Both the experimental and the numerical FSDs are composed of the three parts, i.e. fine-fragments, intermediate size fragments, each described by a separate fragmentation mechanism and ditto power-law exponent, and boulders. Here, the fines arise as a result of the crushing-shearing mechanism. The branching-mergings of tensile cracks are responsible for the creation of the intermediate size fragments. Major tensile cracks delineate the boulders. Furthermore, the spatial location of the fines with respect to a blast-hole is studied using the HiDEM code. The absolute mass of the fines is calculated as a function of their distance to the blast-hole. The HiDEM results supported by experiments show that the major amount of fines is not created at or around the blast-hole as the Crush Zone Model assumes. In the third part, 24 FSDs from controlled blasting tests, which were either unconfined or confined by momentum traps are reported. High-resolution HiDEM simulations of a pressurized crack propagating in a heterogeneous brittle medium are performed, and the FSDs are computed. The pressurized crack is subjected to different external lateral stresses in tension and compression to mimic different scenarios that may arise in blasting tests. In the simulations, the power-law exponent of the size distribution in the fines region depends on the external stress states. That means, the fines power-law exponent at high compressive lateral stresses has a crushing-shearing origin of fragmentation, while at low compressive or tensile lateral stresses the exponent has a branching-merging origin of fragmentation. In the tests, the FSDs consist of two branching-merging terms in the fines and intermediate size fragments regions, and a boulders term, i.e. the previous crushing-shearing mechanism acting in the fines region is replaced by a second branching-merging one. In conclusion, the main mechanism forming the fines is a function of external stresses or confinement conditions. At high external compressive stresses the majority of fines are formed by compressive crushing-shearing. The branching-merging, on the other hand, is the main mechanism at tensile and low compressive external stresses.