Abstarct: In order to investigate the identity of the gorening internal nuclear interactions of the few-nucleon systems, and the study of structural properties of bound state of these nuclei, in this thesis we have solved the few-nucleon bound systems from 3-nucleon up to 6-nucleon bound systems within the Faddeev-Yakubovsky (F-Y) approach in momentum spce representation, in both Partial-Wave (PW) and Three-Dimensional (3D) formalism with the inclusion of spin-independnet and spin-dependnet Nucleon-Nucleon potential models. The F-Y formalism by applying the Schrodinger equation, transforms to some coupled equations in terms of some independent amplitudes. The achievements of 2-nucleon and 3-nucleon systems within the F-Y methods, demonstrate that a direct treatment of 5-nucleon and 6-nucleon systems is accessible on today’s computers with high computational speed. Therefore, in order to solve the 6-nucleon problem, we feel that an accurate and old reliable method, the exact solution within the Yakubovsky equations, is now desirable. In addition, we have solved the coupled F-Y equations for 5-nucleon and 6-nucleon bound systems in case of the effective α-core structure in partial-wave and three-dimensional representation implemented in the basis of momentum variables. We formulated the coupled Yakubovsky equations first for spinless particles as function of Jacobi momenta, namely the magnitudes of the momenta and the angles between them. The coupled integral equations for a bound-state can be handled in partial-wave representation and solved by a numerically reliable standard method. Our numerical results for spin-independent NN interaction potential are in good agreement with results of other methods in the first step calculations and the little obtained binding energy difference between 4- , 5- and 6-nucleon bound systems, confirms the halo structure of six-body bound system in case of effective α-core structure. The Yakubovsky equations for light nuclie are some coupled equations in terms of some Yakubovsky components that can be represented in momentum spapce baxsed on the Jacobi coordinate, in PW and 3D formalism. Our aim in this thesis is to extend the F-Y approach on the basis of PW and 3D representation with basis states in terms of the Jacobi momenta for exact solution of the 5N and 6N bound-state problem with NN interactions. We have found it natural to use the standard PW and 3D representation essentially because of dealing with scalar variables. We investigate the 5N in the picture of effective alpha-nucleon structure and 6N effective halo structure bound systems, namely an inert α-core and two loosely bound nucleons. In the numerical implementations, the technical performance in PW and 3D decomposition is implemented, different set Jacobi momenta as well as a necessary multi-dimensional interpolation scheme are given, like modified cubic Hermit splines. In order to solve the high dimensional energy eigenvalue problem of the coupled equations for the systems in case of effective α-core structure, we point to the Lanczos-type algorithm, which turned out to be very efficient in the 3- and 4-nucleon problems, using typical iteration method. The acheivments and outcomes of this thesis with respect to the regarded some spin-independnet and also spin-dependnent NN potential models, in comparison of abtained from oher methods, confirms that the study of few-nucleon bound systems baxsed on the Yakubovsky scheme is successful and desirable. Also, in order to test our numerical claculations we have investigated the convergence of eigenvalue results and also calculated the expectation value energy. This calculation and test of numerical calculations is the final step to the study of few-nucleon bound systems in our thesis.