A cantilever beam used in an Atomic Force Microscope is optimized with respect to two different objectives. The first goal is to maximize the first eigenfrequency while keeping the stiffness of the probe constant. The second goal is to maximize the tip angle of the first eigenmode while again keeping the stiffness constant. The resulting design of the beam from the latter optimization gives almost the same result as when maximizing the first eigenfrequency. Adding a restriction on the second eigenfrequency result in a significant change of the optimal design. The beam is modelled with 12 DOF beam finite elements and the optimizations are carried through with either SLP (Sequential Linear Programming) or MMA (Method of Moving Asymptotes) and similar results are obtained.