The Mostar index of a graph G is defined as the sum of absolute values of the differences between n u and n v over all edges uv of G, where n u and n v are respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. We identify those trees with minimum and/or maximum Mostar index in the families of trees of order n with fixed parameters like the maximum degree, the diameter, number of pendent vertices by using graph transformations that decrease or increase the Mostar index