A circular cylindrical and an oblate cylindrical perfect lens are designed by using coordinate transformation theory. Theoretical analyses are performed to give an insight into the variant angular magnification in the oblate cylindrical perfect lens. We further take advantage of the oblate cylindrical coordinate system to make the object surface flat for future practical imaging and lithography applications. We also for the first time make systematical simulations of various kinds of perfect lens, including numerical confirmation of Mankei Tsang's statement about the magnification of the planar perfect lens and the imaging and magnifying performance beyond the diffraction limit of our designed perfect lens. All the calculated results agree well with our mathematical derivations, thus verifying the coordinate transformation method in designing perfect lenses. (c) 2008 Optical Society of America.