Plant hormone auxin is a key regulator of growth and development. Auxin affects gene expression through ARF transcription factors, which bind specifically auxin responsive elements (AuxREs). Auxin responsive genes usually have more than one AuxRE, for example, a widely used auxin sensor DR5 contains seven AuxREs. Auxin responsive regions of several plant genes have been studied using sets of transgenic constructions in which the activity of one or several AuxREs were abolished. Here we present the method for analysis of the datasets on promoter activity assays having promoter sequences, namely, number and sequences of AuxREs, altogether with their measured auxin induction level. The method for a reverse problem solution considers two extreme models of AuxRE cooperation. Additive model describes auxin induction level of a gene as a sum of the individual AuxREs impacts. Multiplicative model considers pure cooperation between the AuxREs, where the combined effect is the multiplication of the individual AuxRE impacts. The reverse problem solution allows estimating the impact of an individual AuxRE into the induction level and the model for their cooperation. For promoters of three genes belonging to different plant species we showed that the multiplicative model fits better than additive. The reverse problem solution also suggests repressive state of auxin responsive promoters before auxin induction. The developed method provides possibility to investigate AuxRE structure-activity relationship and may be used as the basis for a novel approach for AuxRE recognition.