Abstract Vierendeel steel truss arches are often used in lighting zones of the spatial roof to obtain good permeability and lighting effects. They are different from conventional steel truss arches in terms of failure mechanism and strength design because they have only transverse tubes without diagonal tubes between chords. The chords of the Vierendeel truss arch undertake axial, bending and shear actions while the transverse tubes only resist the bending action. Hence, their structural design against strength is different from conventional steel truss arches. However, this aspect is not well analyzed in literature. This study analyzed the in-plane instability mechanism, failure mode and corresponding strength of the Vierendeel truss arch under a uniform radial load, a full-span uniform vertical load, a half-span uniform vertical load and their combinations. The global in-plane elastic buckling load of the arch under a uniform radial load is derived firstly and an interaction design formula for predicting the global in-plane strength of the arch under a uniform axial compression is proposed. It is found that the chords of the arch may fail in fully sectional plastic moment mode. Transverse tubes may fail because of the end moments. Slender enough arches may also undergo global failure. Strength design equations for local chord failure and for global failure of arches are developed. All of the equations proposed for predicting global in-plane elastic buckling, global in-plane ultimate strength and chord local strength of the arch agree quite well with the finite element results.