Advanced composite arches can deliver superior mechanical performance to fulfil the criteria of the modern engineering design. Functionally graded material (FGM) and nano-reinforced materials are two of the most efficient advanced composite materials. Because of the material property varies continually in the cross-section, the structural analysis is very challenging comparing to homogeneous materials. This dissertation aims to develop an analytical framework in the static behaviour of FG arches and nano-reinforced arches. Firstly, the linear static responses and the geometric nonlinear static responses are analysed; the significant of the geometric nonlinear analysis is stated by result comparison. Secondly, the static buckling analysis is conducted; particularly, two buckling modes are discussed, which are the limit point buckling and the bifurcation buckling. Finally, the equilibrium paths are illustrated in different buckling scenarios. Energy methods are adopted to establish the equilibrium differential equations. To verify the results of the proposed methods, numerical models are developed by using finite element analysis (FEA) software ANSYS. In the FE modelling, the cross-section of the arch is discretised into multiple layers to simulate the variation of the material property. From the numerical verification, the proposed analytical solution agrees well to the numerical models. Furthermore, a renovative nano-composite arch – the Functionally Graded Porous - Graphene Platelets Reinforced (FGP-GPLRC) arch is proposed in this research. By using the proposed analytical equations, the static responses and buckling behaviours is well analysed. From the results, the proposed FGP-GPLRC arch has an impressive strength-weight ratio against buckling. Compare to homogeneous arches, the FGP-GPLRC arch has a significant reduction in the self-weight without scarifying the buckling capacity. This dissertation makes a notable contribution to those design engineering where requires a high strength arch structure with strict size or weight limitation. Also, it provides a useful references and benchmarks for the researchers in the area of advanced composite arches.