A combination of the vortex method and the boundary element method is used here to predict the two-dimensional flow field around a circular cylinder. Cylindrical structures experience strong hydrodynamic loading, due to vortex detachment from the both sides of cylinder during the flow. Thus, the practical meaning of such calculation is significant particularly in offshore oil and gas engineering as well as in the bridge and hydraulic structure engineering. This paper presents the mathematical formulation of the vortex method for the velocity and vorticity field calculation. The calculated velocity and vorticity fields are then used to predict the pressure distribution on the cylinder surface by the boundary element method. The resulting pressure on the cylinder, the Strouhal number and the length of the base recirculation zone are compared with solutions of other numerical methods and experiments, and a good agreement is achieved.