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Abstract The buckling of a nanoplate at the bottom of a channel over which the fluid passes with a one‐dimensional flow is investigated in this article. Navier–Stokes equations were used to obtain the applied force from the fluid to the nanoplate. Non‐local elasticity theories and surface effects were used to consider nanoscale effects. By solving this problem using Galerkin's weighted residual method, interesting results were obtained. Applying non‐locality increases the fluid's impact on the buckling of a nanoplate. The lower modes are more noticeably affected by being placed in a fluid environment. Also, the presence of fluid and surface effects both increase the buckling capacity of the system. The obtained results are very helpful for developing and improving the performance of fluid‐coupled nanostructures that have buckling potential.