Abstract: Strength（failure）theory for geomaterials is an important and essential problem in civil,hy-draulic,mining,railway and highway engineering et al. Each one of present strength theories or failurecriteria can be adapted for only one kind of material. There is much need of a unified strength theorywhich can be adapted for all Kinds of materials,and also need to establish the relationships betweenvarious strength theories. Based on the unified model of twin shear element,and taking accout of allstress components acted on the twin shear element and their different influences on failure of materials,an unified strength theory and unified mathematical expressions are presented in this paper.This newtheory may be referred as twin shear unified strength theory or simplified as unified strength theory.Itcan also be expressed identically in terms of the cohesion parameter C₀ and internal-friction angle φ ofthe materials. It establishes the relationships between various strentth theories,It can be adapted formany kinds of geomaterials and other materials.Those well-known strength theories,yield criteria,andsmooth empiric criteria are the special cases and linear approximations of the twin shear unifiedstrength theory.