Benefiting from the coupling between the Surface Nanoscale Axial Photonics (SNAP) microcavity and the waveguide, i.e., influenced by their abrupt field overlap, multiple axial modes in the transmission spectrum form a functional relationship with the coupling position, thus enabling displacement sensing. However, this functional relationship is complex and nonlinear, which is difficult to be fitted using analytical methods. We introduce a back-propagation neural network (BPNN) to model this functional relationship. The numerical results show that the multimode sensing scheme has great potential for practical large-range, high-precision displacement sensing platforms compared with the single-mode sensing based on the whispering gallery mode (WGM) resonators.