A new spherical tokamak, the SMall Aspect Ratio Tokamak (SMART), is currently being designed at the University of Seville. The goal of the machine is to achieve a toroidal field of 1 T, a plasma current of 500 kA and a pulse length of 500 ms for a plasma with a major radius of 0.4 m and minor radius of 0.25 m. This contribution presents the design of the coils and power supplies of the machine. The design foresees a central solenoid, 12 toroidal field coils and 8 poloidal field coils. Taking the current waveforms for these set of coils as starting point, each of them has been designed to withstand the Joule heating during the tokamak operation time. An analytical thermal model is employed to obtain the cross sections of each coil and, finally, their dimensions and parameters. The design of flexible and modular power supplies, based on IGBTs and supercapacitors, is presented. The topologies and control strategy of the power supplies are explained, together with a model in MATLAB Simulink to simulate the power supplies performance, proving their feasibility before the construction of the system.