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The aggregation of fine or ultrafine particles in liquid due to the nanobubble (NB) bridging capillary force is a key process for many industrial applications. The magnitude and direction of the NB capillary force (NBCF) are directly affected by the geometry of the NB gas bridge between two adjoining particles. Although the NBCF can be accurately measured using experimental techniques, it is very challenging to monitor the images of a NB capillary bridge in nanoscale spatial resolution in NBCF measuring experiments. As a result, the capillary force model that predicts the dependence of the NBCF on the geometry of the NB bridge has never been explicitly verified using experimental means. In this work, molecular dynamics (MD) simulations are carried out to study the NBCF between two parallel plates. MD simulations can readily measure both the NB bridge geometry and the resulting NBCF, which allows us to explicitly verify the predictions from the capillary force model. Our modeling results show that the capillary force model gives a good prediction of the NBCF for both concave and convex NB capillary bridges. Furthermore, with the assumption of constant contact angle and number of gas atoms inside the capillary bridge, we develop an improved capillary force model, which predicts the variation of the bridge geometry and the NBCF with the separation between two parallel surfaces. The continuum predictions from the improved capillary force model are corroborated by the MD simulation results and are consistent with the existing experimental data on NBCFs between two solid surfaces.