This paper states on the new concept of the generalized Bouguer anomaly (GBA) that is defined upon the datum level of an arbitrary elevation. Discussions are particularly focused on how to realize the Bouguer anomaly that is free from the assumption of the Bouguer reduction density ρ B , namely, the ρ B -free Bouguer anomaly, and on what is meant by the ρ B -free Bouguer anomaly in relation to the fundamental equation of physical geodesy. By introducing a new concept of the specific datum level so that GBA is not affected by the topographic masses, we show the equations of GBA upon the specific datum levels become free from ρ B and/or the terrain correction. Subsequently utilizing these equations, we derive an approximate equation for estimating ρ B . Finally, we show how to compute a Bouguer anomaly on the geoid by transforming the datum level of GBA from the specific datum level to the level of the geoid. These procedures yield a new method for obtaining the Bouguer anomaly in the classical sense (say, the Bouguer disturbance), which is free from the assumption of ρ B . We remark that GBA upon the ρ B -free datum level is the gravity disturbance and that the equation of it has a tie to the fundamental equation of physical geodesy.