Current innovations in Magnetic Resonance Imaging (MRI) aim to improve image production (increase resolution or contrast, reduce acquisition time), which can be achieved through an increase of the intensity of the main static magnetic field in the scanner, for example up to 14 T for whole-body MRI [1]. However, reaching such high magnetic fields leads to considerable Laplace forces on the coils, enough to compromise their integrity. This mechanical constraint becomes so predominant at high fields that it calls for a rethinking of electromagnet design methods. This study proposes to solve this design problem through Topology Optimization (TO) in order to produce functional, self-supporting electromagnets. The proposed TO method aims to minimize the volume of the coil while respecting operating constraints, which are antagonistic and come from different physics. On the one hand, the magnetic constraint means that the magnetic field in the imaging region be both sufficiently intense (14 T) and homogeneous (≤ 1 ppm peak-to-peak discrepancy in the field intensity over the imaged volume). On the other hand, the mechanical constraint requires that local von Mises stress must not exceed an elastic limit imposed by the conductor used for the electromagnet. This problem is solved using a coupled magneto-mechanical finite element model of the coil and a density-based TO approach. Particular attention is paid to the treatment of Laplace forces in the sensitivity analysis, being a nonlinear and non-local design-dependent load. The magnetic constraint is treated by the spherical harmonic decomposition [2] of the magnetic field over the imaging region and the singular mechanical constraint is regularized either by an aggregation function or a damage approach [3]. The first 14 T coil designs obtained by TO presented in this article respect the magneto-mechanical constraints but their cross-section should be further improved through additional manufacturing considerations. Our algorithm is also evaluated by comparing obtained solutions for lower 11.7 T magnetic fields to currently existing MRI scanners. [1] M.E. Ladd, et al. https://doi.org/10.1007/s10334-023-01085-z [2] Garrett, M. W. https://doi.org/10.1063/1.1700115 [3] A. Verbart, et al. https://doi.org/10.1007/s00158-015-1318-9