This paper presents the fundamental principles of robust maximum likelihood invevse method for gravity and magnetic interprtation devoloped by Joao B. C. Silva(1989).The inversion of nonlinear geometric parameters of 2-Dgravity body is discussed and extended into the inversion of nonlinear geomotric parameters of 3-Dgravity and magnetic body.Emphasis is put on the inversion result under the influence of major random noise and a variety of geological noise sources in the field. Result from theoretical inversion suggests that this method has a solution closer to reality than the least square inversion procedure: therefore, it increases the reliability of solution and supplies a fairly good inversion result for local and isolated gravity and magnetic anomaly.