Numerical prediction of crack growth and damage are long-standing problems in compu- tational mechanics. The difficulties inherent in these problems arise from the basic incom- patibility of cracks with the partial differential equations that are used in the classical theory of solid mechanics. The spatial derivatives needed for these partial differential equations to make sense do not exist on a crack tip or surface. Therefore, any numerical method derived from these equations inherits this difficulty in modeling cracks. The peridynamic theory of mechanics attempts to unite the mathematical modeling of continuous media, cracks, and particles within a single framework. It does this by replacing the partial differential equa- tions of the classical theory of solid mechanics with integral or integro-differential equations. Theoretical and numerical analysis based on the deterministic and stochastic peridynam- ics model will be studied, relevant numerical experiments will be conducted to show the effectiveness of the proposed methods.