Equivalent Uniform Dose (EUD) for tumors is defined as the biologically equivalent dose which, if given uniformly, leads to the same cell kill in the tumor volume as the actual non-uniform dose distribution. Recently it has been generalized to include normal tissue as well. Typically EUD is between the minimum and mean dose for critical structures end it is between the mean and maximum dose for tumors. EUD can be a useful endpoint in evaluating treatment plans with non-uniform dose distributions for 3D conformal radiotherapy (3DCRT) and intensity modulated radiotherapy(IMRT), In this study we investigate the feasibility of using the generalized EUD in the objective functions for IMRT optimization, We applied the EUD based optimization to a group of head and neck cancer patients and compared plans with those generated with dose-volume based criteria. We found that the EUD based optimization improves the sparing of critical structures while maintaining the same or better target coverage. Since EUD for tumors is not sensitive to the "hot spot", the target dose distributions are more inhomogeneous. While this may be considered beneficial for some sites, it is not generally acceptable. To circumvent this, we treated the target as a type of normal structures with constraints on the maximum dose. This lead to a much-improved target dose homogeneity with minimal effect on normal structures, Our preliminary investigations indicate that EUD based optimization can be a viable alternative to the currently widely used dose- and dose-volume based optimizations.