Abstract When the Lame coefficient and unit vector which characterize the strain tensor of Cartesian coordinates are given anew and substituted into orthogonal curvilinear coordinates it is found that the strain tensor in Cartesian coordinates is the function of Lame coefficient and unit vector.Using the transformation matrix between the Cartesian coordinates and orthogonal curvilinear ones we have deduced the mathematical expression of the corection for the displacement differential of orthogonal curvilinear coordinates and given the genenal expression of the strain tensor in this coordinates.
