In this study, various sandwich panel structures with different reticulate lattice core geometries were designed and then fabricated in titanium via the electron beam melting (EBM) process. Bending tests were performed on the titanium samples, and mechanical properties such as modulus, bending strength, and energy absorption were evaluated. Different failure mechanisms were observed, and it was found that sandwich structures with auxetic cores exhibited more homogeneous deflection and bending compliance compared with other structures. It was also demonstrated that properties of auxetic sandwich structures can be tailored using different cell structure geometries to suit the needs of a given design application. Furthermore, it was found that other 3D cellular sandwich structures can also exhibit high stiffness and strength, which is desirable in potential applications.