Several algorithms have been developed for computing the potential and attraction of a simple density layer; these are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density (5¿¿5¿) blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.