This work intends to simulate numerically the external flow of incompressible laminar stream at steady state for low Reynolds numbers around a cilindrical body. The solution of the present problem is obtained by means of the resolution of the equations of conservation of mass and momentum. The present numerical method to solve the equations of conservation is a combination of the lagrangian method of the characteristics, and the method of finite volumes. A curvilinear system of coordinates is selected to adapt to the body geometry. The mesh is generated based on the potential flow solution around the cylinder. Once performed the numerical computation, the velocity profile, the pressure and shear stress distribuitions around the cylinder are analysed. The determination of the drag from the data on dynamic pressure and viscosity effects around the cylinder is also done. The local and average results are compared with the experimental and numerical results available, with a reasonable agreement.