Total field magnetic anomalies can be computed for groups of two-dimensional bodies of irregular cross section by assuming each body to be either bounded by a bundle of magnetic pole lines or enclosed by a set of planes within which the surface density of magnetic poles is a constant. Increasing the number of pole lines through use of an interpolator improves the quality of the pole-line method and makes it very useful for computing the anticipated magnetic effect from shallow, high-magnetization bodies whose surfaces are essentially nonplanar. This paper describes a computer procedure which uses both the pole-line and bounded-plane techniques, presents the computer program and its development, and gives examples of its use. The ability of the method to affect two-dimensional terrain corrections in lava-covered areas is demonstrated by a realistically modeled lava tube whose anomaly could not have been seen reliably if terrain effect had not been removed.