Background: Biological approaches to intervertebral disc (IVD) restoration and/or regeneration have become of increasing interest. However, the IVD comprises a viscoelastic system whose biological replacement remains challenging. The present study sought to design load-sharing two-component model systems of circular, nested, concentric elements reflecting the nucleus pulposus and annulus fibrosus. Specifically, we wanted to investigate the effect of architectural design variations on (1) model system failure loads when testing the individual materials either separately or homogeneously mixed, and (2) also evaluate the potential of modulating other mechanical properties of the model systems. Methods: Two sets of softer and harder biomaterials, 0.5% and 5% agarose vs. 0.5% agarose and gelatin, were used for fabrication. Architectural design variations were realized by varying ring geometries and amounts while keeping the material composition across designs comparable. Results: Variations in the architectural design, such as lamellar width, number, and order, combined with choosing specific biomaterial properties, strongly influenced the biomechanical performance of IVD constructs. Biomechanical characterization revealed that the single most important parameter, in which the model systems vastly exceeded those of the individual materials, was failure load. The model system failure loads were 32.21- and 84.11-fold higher than those of the agarose materials and 55.03- and 2.14-fold higher than those of the agarose and gelatin materials used for system fabrication. The compressive strength, dynamic stiffness, and viscoelasticity of the model systems were always in the range of the individual materials. Conclusions: Relevant architecture-promoted biomechanical performance-tuning of tissue-engineered constructs for biological IVD replacement can be realized by slight modifications in the design of constructs while preserving the materials’ compositions. Minimal variations in the architectural design can be used to precisely control structure–function relations for IVD constructs rather than choosing different materials. These fundamental findings have important implications for efficient tissue-engineering of IVDs and other load-bearing tissues, as potential implants need to withstand high in situ loads.