Ultralight sandwich constructions with corrugated channel cores (i.e., periodic fluid-through wavy passages) are envisioned to possess multifunctional attributes: simultaneous load-carrying and heat dissipation via active cooling. Titanium alloy (Ti-6Al-4V) corrugated-channel-cored sandwich panels (3CSPs) with thin face sheets and core webs were fabricated via the technique of selective laser melting (SLM) for enhanced shear resistance relative to other fabrication processes such as vacuum brazing. Four-point bending responses of as-fabricated 3CSP specimens, including bending resistance and initial collapse modes, were experimentally measured. The bending characteristics of the 3CSP structure were further explored using a combined approach of analytical modeling and numerical simulation based on the method of finite elements (FE). Both the analytical and numerical predictions were validated against experimental measurements. Collapse mechanism maps of the 3CSP structure were subsequently constructed using the analytical model, with four collapse modes considered (face-sheet yielding, face-sheet buckling, core yielding, and core buckling), which were used to evaluate how its structural geometry affects its collapse initiation mode.