Based on the Sombor index of graphs defined by Gutman in 2021, Shetty and Bhat defined the Sombor index of hypergraphs recently. Inspired by the work of Deng et al. [Int. J. Quantum Chem. 121 (2021) e26622] and Vukićević [Math. Montisnigri. 50 (2021) 5-14], we characterize the extremal hypergraph with the upper and lower bounds of Sombor index for \( k \)-uniform chemical hypergraphs with \( n \) vertices and give the corresponding value of Sombor index. Furthermore, we characterize the extremal hypergraph with the upper bound of Sombor index for \( k \)-uniform chemical hypertrees with \( n \) vertices and give the corresponding value of Sombor index.