In this study, we focus on the application of global sensitivity analysis (GSA) to gain insight into the influence of model parameters on the outputs of multispecies contaminant transport model. In this context, employing GSA methods (Morris and FAST) allows us to comprehend the relative significance of each input parameter in the model. We specifically analyzed the effects of model parameters on the concentration breakthrough curves and associated temporal moments of concentration of contaminant species. The spatial variability of sensitivity indexes from Morris and FAST methods for parent and daughter contaminant species is also investigated. We represent uncertainties of longitudinal dispersivity, porosity, first-order degradation constants of parent and daughter contaminant species, and sorption distribution coefficient of parent species into the coupled multispecies contaminant transport model and GSA framework. Our results show a complex interplay between different model parameters and their varying influences on different output metrics. The ranking of parameters based on GSA shows that (i) the contaminant mass recovery of final daughter species of three species chain reaction is governed by the first-order degradation coefficient of parent and first daughter species; (ii) dispersivity and porosity are critical parameters that govern the mean residence time and variance of breakthrough curve of final daughter species; (iii) the coefficient of skewness is more sensitive to dispersivity, sorption distribution coefficient, and first-order degradation coefficient of parent species as compared to other model parameters. The variation in the sensitivity indices among contaminant species and with travel distance is observed. This study highlights the significance of global sensitivity analysis when simulating the multiple species contaminants in saturated porous media.