The fundamental understanding of the flow inside Progressive Cavities Pumps (PCP) represents an important step to improve the efficiency of these pumps in the petroleum artificial lift industry. The simulation of the flow in the PCP is extremely complex due to the transient character of the flow, the moving boundaries and the difference in length scale of the channel height between the stator and rotor. This complexity makes the use of CFD as an engineering tool almost impossible. This dissertation presents an asymptotic model to describe a single phase flow through progressive cavities pumps, using the lubrication theory approach. The model was developed for Newtonian fluid and the lubrication theory was used to reduce the three-dimensional Navier-Stokes equations to a two-dimensional Poisson´s equation for the pressure field. The models differential equations were written in cylindrical coordinates and were numerically solved by the finite difference method. A program was developed in Matlab and the results reproduce the experimental data, with a significantly shorter processing time, which is orders of magnitude faster than the model that solves the complete set of equations. The results show the effect of geometry and operational parameters, such as the clearance between stator and rotor, the number of pitches, viscosity and density of the fluid, rotation and differential pressure, in the pump performance curves.