The solution of the problem of a penny-shaped crack in an inhomogeneous material with elastic coefficients which are varying continuously along the direction perpendicular to the crack is examined in this paper. We studied the problem for an inhomogeneous material which satisfies the conditions of either torsional deformation and normal extension. A series form solution to the problem is proposed and analytical expressions for the first two terms of the series are obtained by using a Hankel transform technique. In the solution a homogeneous body is chosen as the reference so that inhomogeneous quantities are treated as being perturbed from the zero's reference solutions. Closed form expressions for the relevant stress intensity factors and the crack energy are derived and specific cases of the problem are also considered. (C) 1999 Elsevier Science Ltd. All rights reserved.