Firstly，the paper proposed the necessity of discussing the non Gauss of gravity and magnetic anomalies signals according to the basic assumptions of the blind source separation and separation conditions. Secondly，it was obtained that gravity and magnetic anomaly signals of the sphere and upright rectangular are not Gauss signals by studying on the Gauss of gravity and magnetic anomalies signals of the different theoretical models. At the same time, it was concluded that whether the gravity and magnetic anomalies of steps is Gauss signals, depends on its depth rather than the direction of magnetization.