In recent times, composite materials are widely applied in the construction industry because of their superior properties compared to traditional materials like steel and concrete. The use of composite materials in defense and infrastructure protective applications to resist high rate dynamic loading conditions has been gaining the interest of a lot of researchers over the previous decade. The limitations involved in studying the behavior of composites when subjected to high rate dynamic loads experimentally generated a need for numerical models that could simulate such complex material behavior. These numerical models are also highly useful in situations where it is difficult to perform direct measurements in experiments. The idea of this thesis originated from an aim to study the behavior of a TNO developed composite laminate with alternate 0-degree and 90-degree ply layup when subjected to out of plane blast loads. Considering the complexities involved in such a loading situation, a simplified test setup that can approximately replicate stress conditions in the composite laminate due to out of plane blast load has been proposed to be designed. This simplified test setup is prepared by performing an angled cut from the composite laminate, thus making the plies off-axis with respect to the global coordinate system of its cross-section. The motivation behind choosing such a test setup is that the interface/s can be loaded by a combination of compressive and shear stresses with axial loading on the specimen. The behavior of the simplified test setup with off-axis angles 30-degree, 45-degree, and 60-degree, when subjected to dynamic compression loads with different rates ranging from quasi-static to high is analyzed in this thesis using the finite element method. The initial parts of the study focus on analyzing the quasi-static failure behavior of the off-axis angled composite specimens with a single critical interface at the center modelled using the rate-independent cohesive law coupled with friction. The later parts of the study focus on analyzing the dynamic failure behavior of the composite specimens. The rate-independent cohesive law with friction is improved by adding a rate-dependency feature based on a Johnson-Cook law. Finally, the dynamic behavior of different off-axis angled composite specimens with critical interface/s modelled using the rate-independent and the rate-dependent cohesive laws with friction when subjected to compression loads with different rates is analyzed. The results obtained from the quasi-static analyses indicate that an increase in the mode-II cohesive strength, mode-II cohesive fracture energy, and interface friction coefficient lead to an increase in the peak load carried by the laminates. An increase in the thickness of the plies of an off-axis angled composite specimen results in a decrease in its peak load and changes its governing failure mechanism. There will be a dominant contribution of local inertia and wave propagation effects in dictating the failure behaviors of the specimens when subjected to compression loads with higher rates. The rate-dependent cohesive law with friction developed in this thesis seemingly captured the rate effects in the off-axis angled composite specimens when loaded in compression at different rates. Finally, it is suggested to design the simplified test setup by performing a 45-degree cut from the original composite laminate to simulate delamination due to compression loads of different rates effectively. But all three simplified setups have to be tested to derive the unique set of interface parameters that dictate the failure behaviors of the specimens.