To address the increasing housing demand in Europe and simultaneously tackle the challenge of creating a more sustainable construction industry, timber modular buildings present an innovative solution. However, before multi-storey modular buildings become a widespread practice, various engineering challenges need to be addressed. Ensuring robustness is one such challenge. This study focuses on the robustness of post-and-beam timber modular buildings, particularly through catenary action. The challenge with ensuring robust catenary action lies in designing connections with sufficient resistance and deformation capacity. This study proposes an optimisation process to determine the required mechanical properties of inter-module connections to enable robustness through catenary action. The principle of a catenary relies on the equilibrium between a vertical point load and the vertical component of the tie force in the deflected floor elements. Larger deflections result in a lower required tension resistance but demand a larger deformation capacity in the components. This study introduces a catenary equation to determine the required tensile resistance in a catenary at a specified elongation, creating a catenary requirement boundary. For a timber modular building to form robust catenary action, the axial force-elongation response in a catenary must meet this boundary. The catenary equation and the force-elongation response of the catenary form the basis of the connection optimisation, as the inter-module connection governs the response. To determine the optimised mechanical properties of an inter-module connection in a timber modular building, a case study was performed on a building consisting of twelve post-and-beam modules in width and five modules in height. To determine the effect of a change in the inter-module connection design on the force-elongation response of the buildings, quasi-static numerical analyses were conducted on 2D models, focussing on the frontal view frame of the building, and the floor plane. The load distribution through the floor system and corresponding deformation were added to the frame model by use of spring boundary constraints, after which the catenary could be examined. As a catenary can be formed by increasing the axial resistance, or its ductility, two optimisation methods were formulated, resulting in a high-strength inter-module connection and a ductile inter-module connection with a fuse. The optimisation process is based on iterations of the inter-module connection design. The resulting high-strength connection required a 143% increase in tension resistance, while the ductile connection relied on a 55% increase in resistance and a 550 mm fuse. This study underscores the complexity and critical importance of correct connection design to ensure structural robustness, emphasising the need for sufficient strength and deformation capacity. While the proposed methodology serves as a valuable tool for optimising connections in timber modular buildings, further research is recommended by including dynamic analyses in the optimisation process and experimental testing of inter-module connections to enhance the accuracy of the models.