A method of utilizing photoelastic fringe patterns for purposes of calculating elastic displacements of stressed members is developed. This method utilizes only the lines of constant principal stress difference and does not require knowledge of the directions of the principal stresses. The method developed should prove useful in many cases where measurements of elastic displacements cannot be carried out conveniently but photoelastic fringe patterns are readily available. As an example, the two-dimensional case of a beam in bending with a change in thickness is treated. The correction that must be applied to simple beam theory is determined.