In this work, Ising model with different interactions on the two dimensional square and Kagome lattice is studied using the high temperature series expansion method. High temperature series expansion of zero field susceptibility of the ferromagnetic Ising model on the square lattice is derived to order 12. The series of zero field susceptibility analyzed by the Pade' approximation method. The critical temperature and critical exponent of the zero field susceptibility of the ferromagnetic Ising model on square lattice calculated. The results showed that with increasing order of series, critical temperatures approached to a specific value which is the critical temperature of the Ising model on the square lattice and this value approximately is equal to critical temperature of the zero field susceptibility of the exactly solved zero field Ising model on the square lattice. Therfore ferromagnetic Ising model on the square lattice showed the phase transition. Using the Pade' approximation , critical exponent of the zero field susceptibility is calculated which is in good agreement with critical exponent of the exactly solved Ising model on the square lattice. Next, high temperature series expansion of the zero field susceptibility of the ferromagnetic and two ferromagnetic and one ferromagnetic and antiferromagnetic interactions of the Ising model on the two dimensional Kagome lattice derived to order 12. These series analyzed by the Pade' approximation method. The results showed that ferromagnetic Ising model on kagome lattice have the ferromagnetic to paramagnetic phase transition. The critical exponents of the ferromagnetic Ising model on kagome lattice have a good agreement with critical exponent of the zero field susceptibility of the exactly solved Ising model on the square lattice. Therefore these two models have approximately same critical temperature. The critical exponents of this model consistent with the universality hypothesis have a good agreement with zero field susceptibility critical exponent of the exactly solved Ising model on the square lattice. But one ferromagnetic and antiferromagnetic interactions of the Ising model on kagome lattice did not show any phase transition because of the frustration. This frustration is related to the geometry of the Kagome lattice. These two models also have similar behavior. The last section, vertex functions and zero field susceptibility of the XY model on the square lattice using the free graph expansions is derived to order 8. Then zero field susceptibility of the XY model on square lattice is analyzed by the Pade' approximation method. The results did not show any phase transition for XY model on square lattice. Key words : Ising model, Kagome lattice, Zero field susceptibility, High temperature series expansion, Free graph expansion, XY model, Ionic disorder