In the last twenty years, composite materials were used in several engineering applications for possessing a good combination of properties. Therefore, researchers are interested in investigating these materials and their classifications, manufacturing, properties and failure. This book is concentrated on failure behavior of composite materials and the goals of this work are: 1. Building a finite element model describing the breakage effect in composite materials and comparing this model with the shear lag model in terms of accuracy of results, computation time and the cases that can be calculated by the models. 2. Studying the distribution process which happens due to the breakage in fiber (or matrix or both) and also studying the effects of the misalignment phenomena on the redistribution process. 3. Using the finite element model to calculate the shear stress along the surfaces between any pair of matrix-fiber in the structure of composite materials, since the shear stress, in previous shear lag models, can not be calculated with good accuracy. This book consists of three sections. Each section deals with several points used to understand the problem studied in this work. Section one (Introduction) deals with general definitions, description, classifications and properties of composite materials. Also, in this section, the failure theories of composite materials are described in order to understand the goal of this work. For the same purpose, composite materials research progress have been presented too. Section two (Theoretical Analyses) is subdivided into three main parts. The first one describes the assumptions, governing equations, method of solution and simulation or programming of the solution of the micromechanical shear lag model. While the second part deals with the finite element model using ANSYS. Where the derivation of the shape functions of the element which is used in the model, general formulation of finite element method and the procedure of building the ANSYS model are described. The final part describes the cases studied in this work. Section three (Results) displays the results calculated using the two models. This section is divided into two parts. The first one discusses and compares the results of the two models in several cases. While the second one discusses the shear stress results in the same cases taken in the first part.