Vertically Aligned Carbon Nanotube (VA-CNT) arrays/turfs are a new class of nanomaterial that possess excellent mechanical, electrical and thermal properties and promise tremendous potential for widespread applications in several areas of engineering. This has triggered an utmost need to understand the behaviors of these nanomaterials to explore and realize their full potential to be able to efficiently design and implement new structures and devices. The approach here is based on Integrated Computational Materials Engineering (ICME), linking material models at nanoscale, mesoscale and structural scale levels. Mechanical responses of both 'template' and 'template-free' grown VA-CNTs resembling that of low density foam beginning with individual nanotube are studied. The architectures and geometric parameters-tube configuration, diameter, height, packing density, tube distribution pattern in the VA-CNTs have been thoroughly examined. The understanding developed will help to further explore the VA-CNT's for several multifunctional applications as in development of flow sensors, supercapacitors, interconnects, hybrid composites, energy generation, storage, dissipation devices and more.