Tied-arch bridges are bridges that have high structural efficiency, but are prone to bending instability. This study aims to analyse the relationship between arc geometry variations and the bending stability of tied-arch bridges using the Finite Element Method (FEM) based on SAP2000 software, employing both linear and non-linear approaches. The linear analysis results show that lateral arch deformation occurs, indicating the potential for global lateral instability of the arch. Meanwhile, the non-linear analysis, which considers the significant geometry effect (P-Δ), produces a bending capacity of 7.43-11.69 kN with a maximum deflection of -0.52 mm. Variations in the arch angle were found to affect the critical bending capacity without significantly impacting global deformation. These findings are expected to serve as a valuable reference for designers and structural engineers in determining optimal and efficient arch designs.