A relatively simple optical method based on Seidel aberration theory was presented for the design of mechanically compensated infrared reflective zoom systems with 4 mirrors. This research includes the study of image formation rules by a single mirror, the concept of the mechanical compensation method in zoom systems, and the derivation of analytical formulae for the Seidel aberration coefficients. The advantage of this method is that it allows the designer to achieve the initial structure parameters of the optical system (radii of curvature and separations between mirrors, etc.) by solving a set of Seidel aberration coefficient functions. Two design examples of 4-mirror zoom systems were given. The results show that the proposed method is feasible in the design of infrared reflective zoom systems with large zoom ratios.