The dominant cost and time driver in unexploded ordnance (UXO) cleanup is the necessity of digging (excavating) “false alarm” gèophysical anomalies. As many as 75% of all the anomalies investigated are false alarms, e.g., scrap metal, ordnance debris, cans, wire, etc. The effort to develop capability to discriminate UXO anomalies from false alarm anomalies is a driver for the development of geophysical model-based signature modeling. The signature modeling is important for forward signature prediction and ultimately for geophysical inversion of buried object parameters from measured data. Researchers are actively developing forward and inverse modeling capability for time-domain and frequency-domain electromagnetic induction, ground penetrating radar, magnetic, and gravity anomaly signatures for realistic UXO shapes. This paper documents progress in developing forward gravity and total magnetic field analytical solutions. Gravity and magnetic methods are passive and share similarity in mathematical formalism. If both gravity and magnetic signatures of UXO can be detected in practice, the potential exists for an integrated bulk density determination as a discriminant. Fundamental concepts of the gravity and magnetic methods as applied to detection and potential discrimination of buried UXO are discussed. Analytical solutions for the gravity and total magnetic field signatures of prolate spheroid models of UXO are developed. The total magnetic field solution is a multipole expansion approximation that includes the dipole and octupole contributions, with the quadrupole contribution zero due to symmetry of the spheroid. The gravity solution is a full analytical solution for the field exterior to a spheroid. Examples and results of application of the solutions to spheroid UXO modeling are presented, along with implications for detection and discrimination. The examples include the effects of spheroid orientation on the signature characteristics. Total magnetic field anomalies of UXO are generally detectable to at least the maximum predicted penetration depths for typical soil types and low background magnetic noise. Gravity anomalies for 105-mm projectiles and larger UXO are detectable at very shallow depths (i.e., just below the surface), but only the very largest UXO (e.g., 14-inch projectiles) will produce detectable anomalies for burial depths approaching 1m.