The analysis of the predictive ability of the Hill quadratic criterion of plasticity has been carried out for monocrystalline nickel based superalloys. The possibilities of determining the parameters of the quadratic criterion on uniaxial tensile tests for single-crystal samples of different crystallographic orientation were investigated. The experimental results and predictions of micromechanical model with the Schmid criterion were compared. In order to improve the prediction accuracy the phenomenological fourth degree criterion of plasticity was proposed, that allowed taking into account a number of effects that could not be described by a quadratic criterion.