A method based on the 3rd-order aberration theory is described for the design of mechanically compensated reflective zoom systems with 3 mirrors. By constrained optimization of a set of Seidel aberration coefficient functions, the initial construction parameters of the optical system can be achieved, and the design results prove the feasibility of this method. The limitation of the above method and the necessity of the design of reflective systems without obscuration are also pointed out. A new design theory is explored which could eliminate obscuration and correct aberrations at the same time.