The structural behaviour of shallow arches is complex and can be influenced by many parameters. In this paper, the response of a half-sine shallow arch under static loading in a thermal environment is investigated. The arch has pinned supports and the material behaviour is assumed elastic. The exact displacement field, load-bearing capacity and the locus of critical points are obtained. Boundaries of domains with different stability behaviours (e.g., different number of limit and bifurcation points) are also determined. Three types of loading (concentrated, uniform and asymmetrical uniform) are examined. The primary equilibrium paths are verified against results obtained from finite element simulations. The proposed method is robust and accurate.