This capter presents a novel method for splitting terahertz (THz) surface waves based on the propagation characteristics of spoof surface plasmon plaritons. Metal disk splitters with a central hole and radially arranged gratings are proposed and analyzed using the FDTD method in cylindrical coordinates. Numerical results show that the disks act as bi- and multidirectional THz surface wave splitters with large coupling regions, the frequency of which is selected by the grating structures. To efficiently analyze cylindrical structures, we further develop the cylindrical hybrid implicit-explicit finite-difference time-domain method, in which the implicit scheme is adopted only in the circumferential direction. The connection of the field in a specific plane gives the cyclic matrix problem, the solution of which is performed with the Sherman-Morrison formula. The convolutional perfectly matched layer is also introduced in cylindrical coordinates. The present method is applied to the analysis of the metal disk type surface wave splitter. The computational time is reduced to less than 20% of the explicit method, yielding almost the same numerical results. The calculated radiation patterns are compared with experimental results at gigahertz frequencies.