In recent years, use of composites is increasing in most fields of engineering such as aerospace, automotive, civil construction, marine, prosthetics, etc., because of its light weight, very high specific strength and stiffness, corrosion resistance, high thermal resistance etc. It can be seen that the specific strength of fibers are many orders more compared to metals. Thus, laminated fiber reinforced plastics have emerged to be attractive materials for many engineering applications. Though the uses of composites are enormous, there is always an element of fuzziness in the design of composites. Composite structures are required to be designed to resist high stresses. For this, one requires a reliable failure criterion. The anisotropic behaviour of composites makes it very difficult to formulate failure criteria and experimentally verify it, which require one to perform necessary bi-axial tests and plot the failure envelopes. Failure criteria are usually based on certain assumption, which are some times questionable. This is because, the failure process in composites is quite complex. The failure in a composite is normally based on initiating failure mechanisms such as fiber breaks, fiber compressive failure, matrix cracks, matrix crushing, delamination, disbonds or a combination of these. The initiating failure mechanism is the one, which is/are responsible for initiating failure in a laminated composites. Initiating failure mechanisms are generally dependant on the type of loading, geometry, material properties, condition of manufacture, boundary conditions, weather conditions etc. Since, composite materials exhibit directional properties, their applications and failure conditions should be properly examined and in addition to this, robust computational tools have to be exploited for the design of structural components for efficient utilisation of these materials. Design of structural components requires reliable failure criteria for the safe design of the components. Several failure criteria are available for the design of composite laminates. None of the available anisotropic strength criteria represents observed results sufficiently accurate to be employed confidently by itself in design. Most of the failure criteria are validated based on the available uniaxial test data, whereas, in practical situations, laminates are subjected to at least biaxial states of stresses. Since, the generation of biaxial test data are very difficult and time consuming to obtain, it is indeed a necessity to develop computational tools for modelling the biaxial behavior of the composite laminates. Understanding of the initiating failure mechanisms and the development of reliable failure criteria is an essential prerequisite for effective utilization of composite materials. Most of the failure criteria, considers the uniaxial test data with constant shear stress to develop failure envelopes, but in reality, structures are subjected to biaxial normal stresses as well as shear stresses. Hence, one can develop different failure… Advisors/Committee Members: Krishna Murty, A V (advisor).