The ellipsoidal Stokes boundary-value problem is used to compute the geoidal heights. The low degree part of the geoidal heights can be
represented more accurately by global geopotential models. So the disturbing potential is splitted into a low-degree reference potential and a
higher degree potential. To compute the low-degree part, the global geopotential model is used and for the high-degree part, the ellipsoidal
Stokes integral is used. I present an effective method to remove the singularity of the spheroidal and spheroidal ellipsoidal Stokes functions
around the computational point. Finally, the numerical results ofsolving the spheroidal ellipsoidal Stokes integral is shown.