For a graph 𝒜 including vertex set V𝒜 and edge set E𝒜, the Sombor index is defined as SO(𝒜) = ∑wz∈E𝒜‍ √η𝒜 (w)2 + η𝒜 (z)2  where η𝒜 (w) is the degree of w in 𝒜.  This study focus on the multiplicative version of SO, namely the multiplicative Sombor index (𝔐SO) which defined as 𝔐SO (𝒜) = ∏wz∈E𝒜‍ √η𝒜(w)2 + η𝒜(z)2. In this work, sharp upper and lower bounds on 𝔐SO of trees in terms of order and given diameter are obtained. We identify the extremal trees for these bounds. Furthermore, the maximal trees are characterized with respect to order and given number of leaves. We determine sharp bounds of simple graphs for 𝔐SO in terms of graph parameters.