Tiny conducting loops are shown to be effective absorbers of microwave radiation. Theory for a single loop is presented. Two theoretical methods are developed for a collection of loops. The first method is an effective medium approach and accounts for particle-particle interactions; a collection of loops is shown to behave as a diamagnetic medium. The second method is only applicable to loops which are relatively far apart and for which interactions are negligible. Both methods are applied to a low density loop chaff cloud and are shown to give essentially the same results. For such clouds the second method is preferred since it is computationally simpler. The first method should be useful for computation of denser compactions of loops. The chaff calculations indicate that a 30 m thick cloud of the specified loops should give more than 15 dB attenuation at 3 GHz (double microwave beam pass through the cloud as would be required for detection of a flat metal plate behind the cloud).