A method for smoothing the measured displacements and computing strains utilizing a finite element method is proposed. Nodal displacement values in a finite element model are determined by fitting the interpolation function inside the elements to the measured values using the method of least-squares. Then, the smoothed displacement distributions are obtained. The displacements in the region where the measured values are not obtained or unreliable are determined by solving finite element equations. The validity is demonstrated by applying the proposed method to displacement distributions of a plate with a hole obtained by finite element analysis and those obtained by electronic speckle pattern interferometry. Results show that the strains can be computed from the measured displacements accurately by the proposed method. Furthermore, the strains near free boundaries and strain concentration region can be determined easily. As strains can be evaluated easily and accurately, it is expected that the proposed method can be applied to various problems in solid mechanics.