Abstract: The geometric midlines of error triangles or gaps between Tresca and twin shear stress yield loci on π-plane were linked up together to form a third yield locus which reflects a new yield criterion called GM (geometric midline) yield criterion in Haigh Westergaard stress space. The mathematical relationship between the GM criterion and its yield locus on π-plane was given as well as an expression of the rate of plastic work done per unit volume. A precision analysis was made with an actually calculated example. It is showed that the GM criterion is a linear one of which the maximum error relative to Mises criterion is not greater than 2.9% with a mean relative error not greater than 0.95%, and its precision is 1% higher than that of MY criterion. As a linear one, its yield locus is a non-equiangular but equilateral dodecagon intersected with Mises locus. The expression of the rate of plastic work done per unit volume of the criterion is also linear.