Internal friction characteristic is one of the basic properties of geotechnical materials and it exists in mechanical elements all the time.However,until now internal friction is only considered in limit analysis and plastic mechanics but not included in elastic theory for rocks and soils.We consider that internal friction exists in both elastic state and plastic state of geotechnical materials,so the mechanical unit of friction material is constituted.Based on study results of soil tests,the paper also proposes that cohesion takes effect first and internal friction works gradually with the increment of deformation.By assuming that the friction coefficient is proportional to the strain,the internal friction is computed.At last,by imitating the linear elastic mechanics,the nonlinear elastic mechanics model of friction material is established,where the shear modulus G is not a constant.The new model and the traditional elastic model are used simultaneously to analyze an elastic foundation.The results indicate that the displacements computed by the new model are less than those from the traditional method,which agrees with the fact and shows that the mechanical units of friction material are suitable for geotechnical material.