We show that dielectric or even perfectly conducting cylinders can be cloaked by a uniform or a layered dielectric cladding, without the need of any exotic or magnetic material parameters. In particular, we start by presenting a simple analytical concept that can accurately describe the cloaking effect obtained with conical silver plates in the visible spectrum. The modeled structure has been originally presented in [S. A. Tretyakov, P. Alitalo, O. Luukkonen, C. R. Simovski, Phys. Rev. Lett., vol. 103, p. 103905, 2009], where its operation as a cloak in the optical frequencies was studied only numerically. We model rigorously this configuration as a multi-layer dielectric cover surrounding the cloaked object, with excellent agreement to the simulation results of the actual device. The concept of using uniform or multilayer dielectric covers, with relative permittivities larger than unity, is then successfully extended to cloaking of impenetrable objects such as conducting cylinders.