To design the vacuum-operated micro/nano-resonator with high quality-factor, the accurate estimation of thermoelastic damping (TED) is of significance. In this work, considering the three-dimensional (3-D) heat conduction as well as the size-dependent and non-Fourier effects in the thermal field, analytical TED expressions for fully-clamped and simply-supported rectangular micro/nanoplate resonators are proposed for the first time. In special, the nonlocal-single-phase-lagging (NSPL) effect of heat conduction is jointly characterized by the nonlocal thermal length-scale parameter and the single-phase-lagging (SPL) time. Firstly, the governing equation of thermoelasticity is modeled under the NSPL model. Especially, the heat conduction along the directions of thickness, width, and length of the plate is taken into account. Secondly, solutions of fluctuation temperature are solved according to the Galerkin approach. Thirdly, utilizing the energy-definition approach, TED models are obtained and expressed in the series form with perfect convergence. Finally, the features of fluctuation temperature with the NSPL effect are investigated, and the influences of the NSPL effect, aspect ratios, boundary condition of constraint, and material type on TED are explored. Simulation results reveal that when the characteristic dimension of plate structure (e.g., the plate thickness) is closer to the nonlocal thermal length referring to the mean-free path of energy carries, the fluctuation temperature and TED of micro/nanoplate with small thicknesses will be significantly affected by the NSPL effect. Moreover, the damping peak of TED spectrum is independent of the aspect ratios. Additionally, the silicon-manufactured micro/nanoplates possess higher values of quality-factor compared with the copper/gold-manufactured micro/nanoplates in most cases.