A new linear yield criterion, referred to as geometrical approximation (GA) yield criterion, is proposed in this paper. On the ${pi}$-plane in Haigh Westergaard stress space, its locus is an equilateral and non-equiangular dodecagon which has the largest approximation to the Mises locus in geometry. Also, its specific plastic work is deduced and applied to the limit analysis of circular plate under uniformly distributed load. Classical yield experimental data are adopted to validate the proposed criterion. It shows that the GA yield criterion can well fit the classical experimental data for different ductile metals. Application of the deduced specific plastic work to the limit analysis of a circular plate shows that the GA-based analytical results are higher than the Tresca results and closely match the Mises numerical results.