The environmental DNA (eDNA) method is the practice of collecting environmental samples and analyzing them for the presence of a genetic marker specific to a target species. Little is known about the sensitivity of the eDNA method. Sensitivity is the probability that the target marker will be detected if it is present in the water body. Methods and tools are needed to assess the sensitivity of sampling protocols, design eDNA surveys, and interpret survey results. In this study, the sensitivity of the eDNA method is modeled as a function of ambient target marker concentration. The model accounts for five steps of sample collection and analysis, including: 1) collection of a filtered water sample from the source; 2) extraction of DNA from the filter and isolation in a purified elution; 3) removal of aliquots from the elution for use in the polymerase chain reaction (PCR) assay; 4) PCR; and 5) genetic sequencing. The model is applicable to any target species. For demonstration purposes, the model is parameterized for bighead carp (Hypophthalmichthys nobilis) and silver carp (H. molitrix) assuming sampling protocols used in the Chicago Area Waterway System (CAWS). Simulation results show that eDNA surveys have a high false negative rate at low concentrations of the genetic marker. This is attributed to processing of water samples and division of the extraction elution in preparation for the PCR assay. Increases in field survey sensitivity can be achieved by increasing sample volume, sample number, and PCR replicates. Increasing sample volume yields the greatest increase in sensitivity. It is recommended that investigators estimate and communicate the sensitivity of eDNA surveys to help facilitate interpretation of eDNA survey results. In the absence of such information, it is difficult to evaluate the results of surveys in which no water samples test positive for the target marker. It is also recommended that invasive species managers articulate concentration-based sensitivity objectives for eDNA surveys. In the absence of such information, it is difficult to design appropriate sampling protocols. The model provides insights into how sampling protocols can be designed or modified to achieve these sensitivity objectives.