Finite Deformation Tensor in Cylindrical Coordinates

Hi, I have been looking at non-linear Elasticity. The components of the finite deformation tensor is defined as F_i_j = partialDiff(x_i)/partialDiff(X_i) with i & j = (1,2,3) With x being the position vector in the deformed state and X the position vector in the undeformed state. I am having troubles with this when using Cylindrical Coordinates. When calculating the components for the torsion and extension of a circular cylinder, i cannot get the correct answer. If any body could run me through calculating the components of this tensor in Cylindrical coordinates i'd very much appreciate it. Cheers Richard