Abstract: This paper first gives the definition of strain vector in elasticity body which is insmall deformation, and points out that the strain state of point in the body is describedby projection forms of the strain vector at this point. and then gives relation betweenstrain vector-stress vector for isotropic elasticity body, moreover derives conditionsthat strain vector coincides with stress vector and the material is incompressible.

Key words: elasticity, small deformation, strain vector, projection, Incompressible