This paper presents the application of the adaptive finite element method (A-FEM) to calculate the thermal fields and ampacity of underground cables in steady state. In respect of mathematics, the Delaunay mesh is developed into the FEM algorithm to make the  adaption of  the grid in the cable surroundings. Its advantage is to obtain the faster solution but still insure the high accuracy. In respect of physics, due to the calculation of thermal distribution in whole system, the readers can realize that the thermal field of any cable can be distorted due to the affect of thermal fields of the other cables and it reflects the essential phenomena of physics (IEC 60287 standard propose that thermal field of any cable is affected by thermal fields of other cables but its thermal field can not be distorted proposes for advantages in calculating using the analytical method). The results of the Ampacity tested for many different configurations of underground cables compared to the ones by boundary element method (BEM) and the real datum of  manufacturer. It has shown the significant reality and  primacy of the proposed method .