The rib-ring type cable dome is a new type of pre-tensioned structure developed by American engineer Geiger according to Fuller's idea of tensile monolithic structure, and it was firstly applied in the gymnasium and fencing hall of Seoul Olympic Games. Considering that the structure is an axisymmetric structure, this paper proposes a fast calculation method to determine the initial prestress distribution. The method starts from the nodal equilibrium relationship of plane radial trusses and derives a generalized formula for the internal force of prestressed rods in rib-ring type cable domes without and with internal tension rings. Tables for the calculation of internal forces are also given for cable dome structures with specific parameters. With the analytical methods, formulas and tables provided in this paper, the initial prestress distribution of rib-and-ring type cable dome structures can be determined easily and quickly, which provides a basis for further design and mechanical property analysis of this type of structures.