In this work, optical profilometry and finite-element simulations are applied on buckled micro-machined membranes for the stress analysis of ion-beam-sputtered $\mathrm{Ta_{2}O_{5}}$ and $\mathrm{SiO_{2}}$ thin films. Layers with different thicknesses are grown on silicon substrates, then several membranes with different geometries are manufactured with standard micro-system technologies; due to a high level of the films' compressive stress, buckled membranes are obtained. Thermally-grown silica membranes are also produced, for comparison. The residual stress values are determined by comparing the measured and simulated deflections of the membranes. The average stress state of the $\mathrm{Ta_{2}O_{5}}$ thin films is found to be $-209$ MPa. The $\mathrm{SiO_{2}}$ thin films are in a higher compressive stress state whose average value is $-576$ MPa. The average stress in thermal $\mathrm{SiO_{2}}$ thin layers grown at 1130 $^{\circ}$C is found equal to $-321$ MPa, in good agreement with the literature.