Abstract The well-known linear relation between the void ratio and the logarithm of pressure for the one-dimensional consolidation has widely incorporated into elastoplastic constitute equation of soils, however, it is not at all straight line for more compressible clays and has several physically unaccepted properties. The compression of clays is explained by fractal theory, and is seen as a balance between the vertical pressure and repulsive force between clay plates. The distance between clay plates depends on the structure formation of the clay flocculation and clay surface. The structure formation of the clay flocculation and clay surface can be modeled by fractal approach. A new formulation of one-dimensional virgin compression of pure clays, expressed by the linear function of ln ν–ln p or ln e–ln p, is proposed based on the fractal model for clay structure. The linear function of ln ν–ln p is suitable to express the virgin compression of the extremely high plasticity clays up to the high pressure of 5000 kPa. For low plasticity clays, the virgin compression satisfies with the linear relationship of ln e–ln p at the pressure higher than 100 kPa. These too are show to be in satisfactory agreement with experimental data. The gradient of the plots of ln ν–ln p and ln e–ln p is related to the fractal dimensions of clay structure, the fundamental material parameters for the first time.