A study is made of magnetic anomalies due to prism-shaped bodies with arbitrary polarization. Expressions of the total field and its first and second derivatives are derived on the assumption of uniform magnetization throughout the body. Formulas for all possible cases in connection with a rectangular prism with vertical sides can be obtained either directly from this paper or by simple extension of the formulas given here. Using the exact expressions given in this paper, the total field and its derivatives are evaluated conveniently and rapidly with the aid of a digital computer. The effect of the dip angle and declination of the polarization vector on the size and shape of the magnetic anomaly is then studied for the case when the earth's normal total field vector has a dip angle of 60 degrees and declination of 0 degrees . With an increase in the dip angle of the polarization vector, the negative anomaly occurring on the north of the causative body diminishes in magnitude, whereas the positive and second derivative anomalies increase to maximum values and then decrease. With an increase in declination, this latter trend is repeated with the positive anomaly but the negative and second-derivative anomalies decrease systematically. Both the positive and second-derivative anomalies become more and more symmetrical with respect to the prismatic body with increase in either the inclination or declination of the polarization vector.