Abstract Axisymmetric free vibrations of moderately thick circular plates described by the linear shear-deformation Mindlin theory are analyzed by the differential quadrature (DQ) method. The first fifteen natural frequencies of vibration are calculated for uniform circular plates with free, simply-supported and clamped edges. Through these computations, the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated, and convergence and accuracy are thoughtfully examined. The case of rigid point support at the plate centre is also considered in the present paper, for which special attention is paid to the capability and convergence of the current method.