Based on the constitutive tensor of the perfect regular polygonal cloak, the effects of different kinds of losses on the performance of regular polygonal cloak are investigated. The cloak is modeled and simulated using full wave package COMSOL MULTIPHYSICS. It is found that if the loss tangents are imposed on one or more components of constitutive tensors, especially on the off-diagonal components, the performance of the cloak in the backward region is significantly different from the results of the traditional case, in which losses are the same in all components of magnetic and electric loss tangents. We believe that the results are helpful for the practical situations.