Abstract Stretched-membrane heliostats provide efficient two-axis tracking mirrors for use in solar thermal applications. The solution of the two-dimensional wave equation for a circular stretched membrane provided lower and upper bounds of the natural frequencies of the heliostat. The effects of the boundary condition on the mode shapes of the membrane were shown in the finite element analysis as well as in the vibration tests. Different natural modes were excited depending upon the number of supports around the circumference of the membrane. Damping in the heliostat was small. Damping ratios estimated from vibration decay curves were less than 3% of critical when the membrane was not stretched and less than 1% when stretched. The bending stiffness of the membrane became significant when the membrane tension was low. The anisotropic effect causing non-uniform membrane tension due to the weldments was negligible.