The prediction with RR’s two invariant Model are smaller than the data, while it can catch the trend of linear increase in band angle with increasing mean stress for fixed values of the least compressive stress and a decrease with increasing values of the least compressive stress.Based on the RR’s two invariant Model, with a Lode angle as the third invariant and the more complicated yield condition, true trixial compression test was carried out.And threeinvariant model was proposed in good agreement between real data and predictions.