Analytical evaluation procedures for determining the acceptability of flaws detected during in-service inspection of nuclear power plant components are provided in Section XI of the ASME Boiler and Pressure Vessel Code. Linear elastic fracture mechanics based evaluation procedures in ASME Section XI require calculation of the stress intensity factor. A method for calculating the stress intensity factor is provided in Appendix A of ASME Section XI. This method consists of a two-step process. In the first step, the stress distribution, as calculated in the absence of the flaw, is obtained at the flaw location. For a surface flaw, the stress distribution at the flaw location is then fitted to a third-order polynomial equation. In the second step, the fitted polynomial representation of the stress distribution is used with standardized influence coefficients to calculate the stress intensity factor. An alternate method for calculation of the stress intensity factor for a surface flaw that makes explicit use of the universal weight function method and does not require a polynomial fit to the actual stress distribution is proposed in this paper for implementation into Appendix A of ASME Section XI. Universal weight function coefficients are determined from standardized influence coefficients through closed-form equations. Closed-form equations for calculation of the stress intensity factor are provided. The technical basis and verification for this alternate method for calculation of the stress intensity factor are described in this paper.