Abstarct: Presenting a comprehensive model for the theoretical investigation of Baryon mass, in a relativistic region or in a nonRelativistic region, has had a particular importance in the recent years. The baryon spectrum is usually described well in all of presented models, although the various models are quite different. What they have in common is the fact that the three quark interaction in baryon can be separated in two parts: the first one, containing the confinement interaction, is spin and flavor independent and it is therefore SU(6) invariant, while the second violates the SU(6) symmetry . In this thesis, we study the spin-, isospin - and flavor - dependent SU(6) violations in the baryons spectrum by using the generalized Gürsey Radicati mass formula (GR). In order to calculate the average energy value of each SU(6) multiplet we have analytically solved the radial Schrödinger equation ( in nonrelativistic model ) and Dirac equation ( in relativistic model ) for our proposed confinement potential. In this study, we regarded the confinement hypercentral potential as a combination of the Coulombic potential, a linear confining potential and the harmonic oscillator potential. The significant characteristic of our model is that not only the confining potential is characterized by the presence of a long range confinement part but also by a short-range potential, which is a Coulombic one, depending on the color charge. The obtained results of the calculations in our proposed model ( the combination of presented approach for solving Schrödinger equation and Dirac equation in the presence of proposed confinement potential as well as using generalized Gürsey Radicati mass formula ) show that the strange and nonstrange baryons mass are in general fairly well reproduced and are much closer to experimental results. Furthermore, our model not only gives a descxription of baryons mass in their ground and excited states with less than 2 GeV mass, but also in most cases is successful in describing the mass spectrum of baryons with more than 2 GeV mass as well as resonance states with negative-parity.