The United States and the Commission of European Communities conducted a series of expert elicitations to obtain distributions for uncertain variables used in health consequence analyses related to accidental release of nuclear material. The distributions reflect degrees of belief for non-site-specific parameters that are uncertain and are likely to have significant or moderate influence on the results. The present work presents the effort to develop ranges of values and degrees of belief that fairly represent the divergent opinions of the experts while maintaining the resulting parameters within physical limits. Where necessary, there is a discussion of correlation coefficients that should be included when the uncertainty is used in a calculation. The methodology used a resampling of the experts' values and was based on the assumption of equal weights of the experts' opinions. Various statistical properties of the distributions, the median, the mean, and the mode, are presented so that the user can choose a parameter value when only a point estimate is desired.