Most laminated composite structures are limited by delamination failures under different kinds of loading. There have been many attempts to develop modeling methodology for delamination under static and dynamic loading. Most early attempts focused on unidirectional laminates due to complexity involved in multi-directional laminates. However, in the real world, most of the time, multi-directional laminates are used. This paper is an attempt to develop such modeling methodology for multi-directional carbon composite laminates (with 0-0, 45-45 and 90-90 interfaces) under static and dynamic loading. For modeling the static loading case, ANSYS15.0 software is used with its built-in, contact-based, cohesive zone material (CZM) model. The mode I and II experiments were also conducted on multi-directional carbon composite coupons as per ASTM standards and the FEA cohesive zone models were validated with experimental loaddisplacement behavior. Mode I and II test coupons are modeled and the delamination is captured in the simulation. For dynamic loading, LS-DYNA is used with built-in tiebreak contact- DYCOSS-Option 9 capabilities, which are similar to the cohesive zone elements. The results show that cohesive zone models can very well predict delamination in this kind of materials under static and dynamic loading conditions. The modeling methodology will be further optimized for both situations to increase robustness and ready for application to composite components in consideration of delamination.