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An analytical expression for the gravitational attraction of a homogeneous polyedral body applying the line integral<br>around its boundary is present here. That effect is calculated by transforming a surface integral into a sum of line<br>integrals using the Stoke’s theorem. The purpose of this work is to illustrate the flexibility of the method for<br>modeling cavities and its application for terrain corrections. The developed theory was applied in the gravimetrical<br>modeling of a shallow karst cavity, contends air, located in the Chapada Diamantina, Bahia, proving the efficiency<br>of the method in this type of problem. The advantage of this numericalmethodologymust it flexibility of smoothing<br>of a polyhedron to the karst body. The results of the modeling will be used in the terrain correction of the data of<br>the effected gravimetrical survey in the area.