The Food Quality Protection Act (FQPA) of 1996 requires the EPA to consider the cumulative risk from exposure to multiple chemicals that have a common mechanism of toxicity. Three methods, hazard index (HI), point-of-departure index (PODI), and toxicity equivalence factor (TEF), have commonly been considered to estimate the cumulative risk. These methods are based on estimates of ED10 (point of departure) and reference doses from the dose-response functions of individual chemicals. They do not incorporate the actual dose-response function of the mixture from multiple chemical exposures. Dose addition is considered to be an appropriate approach to cumulative risk assessment because it assumes that the chemicals of interest act in accordance with a common mode of action (a similar action). This paper proposes a formal statistical procedure to estimate the cumulative risk by fitting the dose-response model of the mixture under dose addition. The relative potency between two chemicals is estimated directly from the joint dose response model of the mixture. An example data set of four drugs representing four chemicals is used to illustrate the proposed procedure and compare it to the HI, PODI, and TEF methods.