Rock mass strength is one of the key factors related to rock mechanics research and rock engineering design. In this paper, rock mass failure is simulated using a discrete Bonded Block Model, BBM, and the rock mass strength is characterized accordingly. A set of optimization algorithms is initially developed to relocate key fractures in the Discrete Fracture Network, DFN, where the distance or intersection angle between two fractures are inappropriate to accommodate regularly sized block elements. The rock mass failure and strength are then simulated using BBM models with varied fracture orientations. Higher strength is generally captured when fractures in the rock mass are less favorable to shear sliding. Since the strength of intact rocks is mechanically stronger than the strength of the initial fractures, the higher rock mass strength results from additional failures of intact rocks. Inherent numerical uncertainties are also characterized when the BBM model is selected for characterizations of the rock mass failure and strength. The strength uncertainty is captured through calibration BBM models, and are attributed to the variations of the block distributions related to fracture accommodations. This strength uncertainty is further increased considering the weakening effects of the fractures. The research addresses several key aspects of using the BBM models for simulations of the rock mass failure, and is expected to characterize the rock mass strength in a more reliable manner.