An inversion procedure, similar to that introduced by Ashour (1974), is given here for obtaining solutions in closed form to two-dimensional electromagnetic induction in plane and cylindrical sheets. The integrated conductivities of these sheets vary as (a2+x2)-1, a≥0 and as (1+&egr; cos &phgr;)-1, 0≤&egr;≤1, respectively, where x is the distance from a fixed line on the plane sheet and &phgr; is the azimuthal angle of the cylinder (a and &egr; are constants). In each case, the conductivity decreases gradually as we go away from a fixed line in the sheet. The sheets are suitable models for certain geomagnetic applications. Numerical results for induction in the cylindrical shell by a uniform inducing field in the direction &phgr;=&pgr;/2 are given when the time variations of the inducing field are either periodic or aperiodic. ¿1990 American Geophysical Union