The present study proposes an analytical solution for the buckling analysis of rectangular nanoplates. In order to extract characteristic equations of the micro/nanoscale plate under in-plane load, the analysis procedure is based on the nonlocal Mindlin plate theory considering the small scale effects. The nonlocal Mindlin plate theory allows for small scale effects. The results show that buckling loads of biaxially compressed micro/nanoscale plate depend on the nonlocal parameter. In addition, the effects of small length scale on buckling loads are graphically presented for different geometrical parameters such as aspect ratios and loading factors. This study might be useful for the design of nanoelectronic devices such as atomic dust detectors and biological sensors.