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WRC Bulletin 501 is the first in a series of Bulletins describing the background for the rules being proposed for incorporation incorporated into the new Section VIII Division 2 of the ASME Boiler and Pressure Vessel Code ("ASME B&PV Code"). PVRC's Task Group on Continued Modernization of Codes sponsored several separate Projects for documentation of the proposed "Div 2- Rewrite" rules. The results of the project on documenting the background for revising the rules for formed heads (tori-spherical and ellipsoidal) in Section VIII Division 2, 0 are reported in this bulletin. It had long been known that the rules of Division 1 were not up-to-date and did not provide uniform safety margins, for the range of geometries and materials. Division 2 rules, based on elastic-plastic analysis, did not include the effect of large deflections in the knuckles of such heads, which stiffen the knuckle and contribute to a much higher pressure capability than the geometrically-linear analyses indicate. Publication of two WRC Bulletins by Professor Arturs Kalnins and Mr. Mahendra Rana; WRC Bulletins 364 and 414 provide background. WRC Bulletin 364 reports on the results of geometrically nonlinear analyses and WRC Bulletin 414 reports on the results of two vessel tests conducted for the PVRC Committee on Piping, Vessels and Nozzles. Based on the results of these studies, The ASME B&PV Code developed new rules for Divisions 1 and 2 of Section VIII published as Code Cases 2260 and 2261, for Divisions 1 and 2, respectively. The rules recommended here are similar to the rules in those Code Cases, with some revisions, most of which are to make the application of the rules easier. One of the features of the Code Cases rules is the inclusion of fatigue criteria for calculating the required design thickness of formed heads. Other Code design-by-rule formulas do not include a consideration of the fatigue failure mode. Therefore, in the proposed rules for Div. 2-rewrite, the fatigue consideration for design of heads has been deleted. This Bulletin reports a number of comparisons between the proposed rules and the existing rules for formed heads, in a number of international codes. Comparisons are also included with the available test results. Comparisons with test results indicate a better agreement for the proposed rules than the rules of other Codes. It is believed that these proposed rules provide a more uniform margin of safety against failure, than other Codes