The instrumented indentation test is an important alternative in quantifying residual stresses. Various indentation models have been developed to determine residual stresses, but no previous models can be applied to a nonequibiaxial residual stress state. To overcome this limitation, a Knoop indentation technique was developed to use the asymmetric characteristics of the Knoop indenter. With the ratio of conversion factors and equations for the relation between the load differences and the residual stress, a model of Knoop indentation was developed to determine the stress directionality p. This model was verified and compared through experiments on various biaxial tensile stress states. Imperfections in the Knoop tip change the conversion factor ratio. Using finite element simulations, this change in the conversion factor was expressed by a fitting equation.