Microdefects such as cracks, vacancies, voids and inclusions are often formed in materials during their manufacturing processes or under working conditions. These defects have significant influences on the mechanical and physical properties of components, especially those for aerospace, automotive and offshore engineering applications, and may eventually result in the damages and failures of these components. Therefore, it is of great importance to investigate the mechanics of materials with these microdefects for the minimization of potential damage and failure of the components. Firstly, a semi-analytic solution is proposed to solve the elastic-plastic fracture behaviors of an infinite space with multiple cracks and inhomogeneous inclusions under the remote tensile stress in this thesis. Based on the Equivalent Inclusion Method, each inhomogeneous inclusion can be modeled as a homogenous inclusion with the initial eigenstrains plus unknown equivalent eigenstrains. The cracks are regarded as a distribution of edge dislocations with unknown densities based on the Distributed Dislocation Technique. By using a modified conjugate gradient method, all the unknown equivalent eigenstrains and dislocation densities are obtained iteratively. The fast Fourier transform and discrete convolution are adopted to improve the computational efficiency. According to the Dugdale model, the plastic zone sizes of cracks can be obtained by canceling the stress intensity factor due to the closure stress and that due to the applied external loading. The effect of the Young's moduli and positions of inhomogeneous inclusions on the plastic zone sizes is investigated.