The rules for performing fatigue assessments of light water reactor pressure vessels and piping are found within Section III-NB and Appendix XIII of the ASME Boiler and Pressure Vessel Code (BPVC). These methods are primarily elastic, utilizing the Tresca-based stress intensity approach to resolve stress amplitudes and, using the design fatigue curve, calculate cumulative usage factors. Elastic-Plastic (EP) analysis rules are prescribed in Appendix XIII and can be used as an alternative fatigue methodology. Currently, Appendix XIII-3440(b) of Section III uses a numerically maximum principal total strain range criteria for EP fatigue analysis, but there are other methods available within other parts of the Code and elsewhere in literature to resolve the EP stress and strain histories for fatigue evaluation. A round robin analysis was organized by the authors to compare some of these alternative EP strain measures against each other and against available test data. Participants evaluated various strain measures for two test articles from a common set of geometry, mesh, and material property information, including prescription of the fatigue curves and environmental enhancement methods to be used in the calculations. The test articles were a thermally shocked stepped pipe and a thick perforated instrumentation ring, both of which have previously been published within the Pressure Vessels and Piping (PVP) Conference proceedings. This paper details the calculations performed by the participants and provides a comparison and contrast of the methods. These results were used to inform proposed changes to the fatigue analysis rules in ASME Section III Appendix XIII that are documented in a companion paper.