Abstract: In this paper an interpolation matrix is proposed for computation of stresses on the element boundary or nodal Points by extrapolation from stresses known for the points within an element. The interpolation matrix is an inverse one of the matrix of the shape functions, and can be formulated by substituting an appropriate portion of the value of the coordinates to the shape functions in matrix. This method gives the same results as that obtained by means of the smoothing matrix proposed by E. Hinton et al. for linear extrapolation with least error. However the interpolation matrix can be easily formulated and is more convenient in computation. Moreover, rusing this method we obtain a solution of non-linear extrapolation. Which better describes the stressesto be determined.