A 3D numerical model of eddy current nondestructive testing （ECNDT） based on the kernel truncated （KT）， adaptive cross approximation （ACA） and singular value decomposition （SVD） algorithms is proposed. It is the first time to apply the KT-ACA-SVD algorithm to accelerate the boundary element method （BEM）-based ECNDT model. The Stratton-Chu formulation is selected， which has no low frequency breakdown issue， as the boundary integral equation. The equivalent surface electric and magnetic field currents， and normal component of the magnetic field are expended by the Rao-Wilton-Glisson （RWG） vector basis functions， and pulse basis functions， respectively. The Galerkin’s method is chosen as the testing method， then the impedance matrix can be achieved. With the help of octree structure， the impedance matrix can be partitioned into diagonal， near and far block interactions which is decided by the distances between them. The diagonal and near block interactions are computed directly by the full matrix method， while the far block interactions are compressed by the KT-ACA-SVD algorithm. Finally， several nondestructive testing （NDT） tests are conducted to compare the impedance variations predicted by the proposed model with the ones achieved by other methods， including analytical， semi-analytical methods， and the experiment. The results demonstrate both the accuracy and efficiency of the proposed model.