An alternating method, in conjunction with the finite element method and a solution for multiple coplanar elliptical cracks in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The solution technique for multiple cracks in an infinite body has recently been developed by the present authors which implements a well-known analytical solution for a single crack in an infinite body. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. Numerical examples are presented for the situation of two equal surface cracks in a pressure vessel. Comparison is made between these results and the procedure for multiple cracks in the ASME Boiler and Pressure Vessel Code.