Recently, the so-called architectured composites have garnered interest in design of materials with enhanced properties. This class of materials offers the opportunity to tune microstructure/geometry along with combination of materials for achieving the properties of interest. Using distinct architectures and altering their design and materials can assist in tailoring mechanical qualities. In this work, the simultaneous stiffness and damping properties, that are otherwise competing in the engineering materials are numerically investigated for two architectures, namely triangle-based, and hexagon-based structures. Finite element analysis of the representative unit cells is performed to obtain the quasi-static tensile response and damping behavior under different frequencies. The simulations are performed with combinations of geometry and different constituent materials. PMMA and PU are used as stiff and viscous materials, respectively, to achieve simultaneous stiffness and damping. The properties are then calculated from the simulation results. It is observed that PU-filled PMMA structure based on triangular geometry offer higher stiffness than the hexagonal geometry, however, reversal of material choice makes the hexagonal geometry favorable for stiffness. This is observed for both when the two geometries with same side length and wall thickness as well as same volume fraction of the materials. In terms of simultaneous stiffness–damping, hexagon-based architecture outperforms its counterpart with same volume fraction of materials. Hexagon with same side length and wall thickness has better simultaneous stiffness–damping than hexagon with same volume fraction.