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For a graph $G$, the Mostar index of $G$ is the sum of $|n_u(e)$ - $n_v(e)|$over all edges $e=uv$ of $G$, where $n_u(e)$ denotes the number of vertices of$G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for$n_v(e)$. We determine all the graphs that maximize and minimize the Mostarindex respectively over all trees in terms of some fixed parameters like thenumber of odd vertices, the number of vertices of degree two, and the number ofpendent paths of fixed length.

Extremal results on the Mostar index of trees with fixed parameters