A new method for modeling of microflows is presented in this thesis. First, the continuum equations of fluid dynamics are developed by using perturbation expansions of the velocity, pressure, density and temperature fields. Subsequently, different orders of equations in dependence of Knudsen number are obtained. Required boundary conditions for solving each order of these equations are obtained by substitution of the perturbation expansions into the general boundary conditions for velocity-slip and temperature-jump. In this research, we use three-therm perturbation expansions and reach to three order of equations O(1),O(Kn),O(Kn 2 ) and their boundary conditions. In fact, the equations of O(1) are the no-slip Navier-Stokes equations. Also, the equations of O(Kn) and O(Kn 2 ) govern required corrections due to the velocity-slip and temperature-jump. This set of equations is discretized in two-dimensional state on a staggered grid using the finite volume method.A three-part computer program has been produced for solving the set of discretized equations. Each part of this code, solve one order of the equations with the SIMPLE algorithm. Incompressible slip micropoiseuille and microcouette flows are solved either analytically or numerically using the perturbation method. The numerical results of the perturbation method are compared with those analytical results. Also, the results of this method are compared with the results obtained from different slip models. In micropoiseuille flow, numerical results agree with analytical results almost for Knudsen numbers lower than 0.03. In microcouette flow, numerical results agree with analytical results almost for Knudsen numbers lower than 0.15. In Both case, numerical results of the perturbation method deviate from its analytical results by increasing the Knudsen number. This reveals that more corrections are needed in the perturbation method by increasing the Knudsen number. But, this approach is computationally difficult and expensive. By two reasons, this problem does not decrease importance of the present work. First, by using of the method presented in this research, it can be completed the slip models and even produced new slip models. For example, the Beskok’s slip model is developed both analytically and numerically. Second, by combination of two slip coefficients and the perturbation method, it can be easily used this method in the high Knudsen numbers. At the end of this research, a shear-driven microcavity flow with slip is investigated and its results are compared with those by the DSMC approach.The investigation of this problem challenges different researcher’s slip coefficients and expresses the need for general and more accurate slip models. Key Words: Microflow,Perturbation method,Slip models, Micropoiseuille,Microcouette, Microcavity