For a graph G, the Sombor index and harmonic index are respectively defined as   (SO(G)=∑uv∈E(G) √(degG2 (u) + degG2 (u)  and H(G) = ∑uv∈E(G)  2/(degG (u) + degG(v), where E(G) is the edge set and degG (u) denoting the degree of a vertex u in G. In this paper, we aim to find extremal trees in the class of chemical trees with the given number of vertices of degree 4 for the Sombor index and the harmonic index. We observe that the extremal chemical trees maximizing the Sombor index also minimize the harmonic index in this class. Furthermore, we construct the corresponding extremal trees.