Summary: In this paper, an efficient adaptive cross approximation (ACA) method is employed for the skin effect and proximity effect analysis. Multi-layer stranded cables with multiple strands and different materials are used for analysis to approximate the effect. The skin and proximity matrices are computed by the ACA low-rank matrix approximation technique. The ACA method can provide better solutions through different iterations. The ACA algorithm is very stable and useful for calculating a low rank matrix approximation, because the adaptive mesh refinement for generating optimal computation. The ACA approach provides the less computational memory and less CPU time. Compare the calculated results with standard work results (such as reference) to verify the effectiveness of the adaptive cross-approximation algorithm.