Traumatic brain injury (TBI) is a serious health and socioeconomic issue which affects thousands of lives annually in the United States. Computational simulations play an important role in better understanding of the TBI and on how it happens. Having accurate material properties of the brain tissue and the elements of the brain will help with more accurate computational simulations. Material characterization is therefore the line on which lots of research have been conducted. In recent years, the emerge of data driven approaches has led to better and more accurate soft tissue characterization. In this dissertation, a metaheuristic search optimization method together with simulation-based optimization framework, and artificial intelligence-based approaches have been employed for macromechanical and micromechanical characterization of brain tissue. First, a constrained particle swarm optimization (C-PSO) technique has been established for soft tissue characterization that overcomes the shortcomings of the classical optimization methods. Through the application of the inherent constraints in the hyperelastic and visco-hyperelastic models, it became possible to reduce the time complexity of this optimization algorithm. Subsequently, the developed constrained optimization method was employed to create simulation-based optimization frameworks for characterizing the micro-level constituents of human brain white matter including axons and extracellular matrix using the hyperelastic and visco-hyperelastic constitutive models. This simulation-based optimization framework helps the researchers to go around the complexities involved with the experimental techniques on micro-level characterization of soft tissues. The final part of this dissertation is devoted to the development of the machine learning and deep learning techniques for classifying the tissue stiffness out of the finite element (FE) simulation results. Through the training of a regularized logistic regression and deep learning convolutional neural networks, it became possible to correctly predict more than 91% of the cases of tissues with high stiffness. The tissues with high stiffness are usually indicative of the pathology and hence are important from medical perspective. The outcome of this part of the work could be useful for qualitative description of the soft biological tissue stiffness and pathology diagnosis which can be used as an alternative to the inversion algorithms.