The output from an eddy-resolved multi-layered circulation model is used to analyze the vertical structure of simulated deep-sea eddies in the Japan Basin of the Japan/East Sea constrained by bottom topography. We focus on Lagrangian analysis of anticyclonic eddies, generated in the model in a typical year approximately at the place of the mooring and the hydrographic sections, where such eddies have been regularly observed in different years (1993--1997, 1999--2001). Using a quasi-3D computation of the finite-time Lyapunov exponents and displacements for a large number of synthetic tracers in each depth layer, we demonstrate how the simulated feature evolves of the eddy, that does not reach the surface in summer, into a one reaching the surface in fall. This finding is confirmed by computing deformation of the model layers across the simulated eddy in zonal and meridional directions and in the corresponding temperature cross sections. Computed Lagrangian tracking maps allow to trace the origin and fate of water masses in different layers of the eddy. The results of simulation are compared with observed temperature zonal and meridional cross sections of a real anticyclonic eddy to be studied at that place during the oceanographic Conductivity, Temperature, and Depth (CTD) hydrochemical survey in summer 1999. Both the simulated and observed eddies are shown to have the similar eddy core and the relief of layer interfaces and isotherms.