This paper presents an analytical three-dimensional breakdown model of SOl lateral power devices with a circular layout. The Poisson equation is solved in cylindrical coordinates to obtain the radial surface potential and electric field distributions for both fully- and partially-depleted drift regions. The breakdown voltages for N~+N and P~+N junctions are derived and employed to investigate the impact of cathode region curvature. A modified RESURF criterion is proposed to provide a design guideline for optimizing the breakdown voltage and doping concentration in the drift region in three dimensional space. The analytical results agree well with MEDICI simulation results and experimental data from earlier publications.