Sandwich panel structures are widely used due to their high compressive and flexural stiffness and strength-to-weight ratios, good vibration damping, and low through-thickness thermal conductivity. These structures consist of solid face sheets and low-density cellular core structures that are often based upon honeycomb topologies. Interest in additive manufacturing (AM), popularly known as 3D printing (3DP), has rapidly grown in past few years. The 3DP method is a layer-by-layer approach for the fabrication of 3D objects. Hence, it is very easy to fabricate complex structures with complex internal features that cannot be manufactured by any other fabrication processes. Due to the recent advancement of 3DP processes, the core lattice configurations can be redesigned to improve certain properties such as specific energy absorption capabilities. This thesis investigates the load-displacement behavior of 3D printable lattice core structures of five different configurations and rank them according to their specific energy absorption under quasi-static loads. The five different configurations are body centered cubic (bcc) diamonds without vertical struts; bcc diamonds with vertical alternate struts, tetras, tetrahedrons, and pyramids. First, both elastic and elastic-plastic finite element analysis (FEA) approach was used to find optimum cell dimension for each configuration. Cell size and strut diameter were varied for each configuration, the energy absorption during compression were calculated, and the optimum dimension was identified for each configuration. Next, the optimized designs were printed using acrylonitrile butadiene styrene (ABS) polymer to evaluate their compression behavior. Fused deposition modeling based Stratasys uPrint printer was used for printing the samples. After printing the samples, all five designs of lattice structures were subjected to compression load and their load-displacement behavior were analyzed and compared. From both FEA calculations and experimental results, the five configurations can be placed as tetrahedrons, pyramids, tetras, BCC diamonds with struts, and diamonds without struts, the first one having the highest and the last one having the lowest energy absorption capabilities. A detailed discussion on the FEA modeling, sample fabrication, and testing of different configurations is presented in the thesis report.