Summary: The magnetic anomaly patterns due to thin lateral deposits of ore can be very similar to those due to deposits in extended magma root structures which potentially may be more important from a geophysical point of view. New forms of the solutions for the anomalous magnetic field due to vertical cylinders and to thin disks are given; these are suitable for fast computation. For various values of the local magnetization vector of the body, the measured anomaly patterns are obtained and features are identified which serve to differentiate the patterns due to a thin disk from those due to a semi-infinite vertical cylinder.