Most materials exhibit different tensile and compressive strains given the same stress applied in tension or compression. These materials are known as bimodular materials. An important model of bimodular materials is the criterion of positive-negative signs of principal stress proposed by Ambartsumyan. This model is mainly applicable to isotropic materials and deals with the principal stress state in a point. However, due to the inherent complexity of the constitutive relation, FEM based on iterative strategy and analytical methods based on a simplified mechanical model are required. In this paper, we review the basic assumptions of this model and its development, several innovative computational methods, and some important engineering applications. We also discuss the sequent key problems in this field.