Numerical solutions have been obtained for incompressible Newtonian flow around a circular cylinder for Reynolds numbers of 1, 2, 4, 10, 15, 30, 50, 100, and 500. The results are presented in the form of vorticity and stream function distributions. The solutions allow detailed characterization of the vortex rings. Drag coefficients, pressure distributions, and vortex dimensions are compared with experimental data and with available theoretical predictions for Reynolds numbers up to 50. The agreement with both experimental data and previous theoretical solutions is considered to be excellent.