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In search for isotropic radiators with reasonable quality Factor (Q), bandwidth, and efficiency, one looks for practical radiators with a typical resonant length of . We present here a Green's function analysis in Fourier of a microstrip element and a far-field integral method in configuration (real) space of single and dual U-shaped elements. Both solutions analytically prove that the power radiation patterns are isotropic in nature (while the thickness and the width tend to zero), although the polarizations are not symmetrical in all cuts. It is also shown that the power isotropic U-shaped radiator, for which the surface current density is infinite, can be replaced by another finite-size radiator, having finite-surface current density, such that its far-field is exactly the same as the far-field of the U-shaped isotropic radiator.