In this paper, an analytical, detailed two-dimensional potential profile model of a newly proposed rectangular core-shell-based double-gate junctionless metal oxide semiconductor (RCS-DGJLMOS) is presented. A detailed numerical solution of the model is presented for conventional n-type double-gate junctionless MOS (DGJLMOS), and the changes made in the model for RCS-DGJLMOS are extensively presented. While solving 2-D Poisson equations, a parabolic potential is assumed along the silicon thickness for both devices. The characteristics of the potential profile are studied on varying doping concentrations, dielectric constants, silicon thickness, and gate oxide thickness in conventional DGJLMOS, whereas the thickness of the core, total silicon thickness, dielectric constants, and core doping are varied in RCS-DGJLMOS. The detailed study on potential profile reveals the huge depletion of RCS-DGJLMOS as compared to conventional DGJLMOS due to the presence of oppositely doped core and, therefore, improves the device performance. Furthermore, the transfer characteristics are also presented for both devices. The analytical results for DGJLMOS and RCS-DGJLMOS have been assessed with Technology Computer Aided Design (TCAD) software. The analytical results obtained from the proposed model are verified with the simulation data.