  For the two-dimensional Schr\"odinger equation, the general form of the point
transformations such that the result can be interpreted as a Schr\"odinger
equation with effective (i.e. position dependent) mass is studied. A wide class
of such models with different forms of mass function is obtained in this way.
Starting from the solvable two-dimensional model, the variety of solvable
partner models with effective mass can be built. Several illustrating examples
not amenable to the conventional separation of variables are given.
