Magnetic flux leakage (MFL) testing is a widely applied method for the ferromagnetic specimen defect detection. In this paper, we present a solenoid analytical model to MFL field based on the molecular current model of a magnetic medium. This model applies $B$ – $H$ characteristics of the material to confirm the homogeneous magnetization of the specimen and to obtain the magnetic moment of solenoids, and then it uses a semi-infinite solenoid as the source to simulate the leakage field. Furthermore, this model proves that the edge effect and defect geometry can be represented properly by setting ellipsoid defects at different positions in the specimen. The results of the proposed model are influenced not only by defect shape as that of the magnetic dipole model but also by the relationship between the magnetization and the normal direction of the defect surface, which leads to the more accurate reconstruction of defects. Based on these findings, the error from the assumption of homogeneous magnetic dipole distribution or magnetization can be explained by the solenoid interaction. This explanation provides a new way to eliminate the computation error, and the solenoid model shows higher computational efficiency compared with the numerical model.