A technique for computing the bending strain resulting from the resonant modal deformation of vibrating plate-like structures is described. Interferometric fringes obtained by time-average holography are used as the basis for generating a mathematically continuous series approximation of a plate-like structure's normal displacement. The terms of the series consist of the clamped-free or free-free eigenfunctions of a simple beam. The bending strain is then obtained by computing the second derivative of the displacement series. The coefficients of the terms of the displacement series are computed for a given segment of a cantilevered plate-like structure based upon the holographic-fringe values lying along the same plate segment. A linear least-squares-solution routine is used to solve for the series coefficients, called modal weighting coefficients, in terms of the normal displacement values obtained from the holographic-fringe value. A ‘best fit’ solution is thus obtained for the plate displacement. This least-squares approach in conjunction with the fact the beam-series functions exactly satisfy the plate's geometric boundary conditions and approximately satisfy the plate's natural boundary conditions, results in a displacement series that yields quite accurate displacement and bending strain values.