This article presents the computer-aided design of the intermediate and input/output cavities of a multi-beam klystron (MBK) working in the J-band frequency range. A coaxial type cavity has been proposed to meet the specified design parameters. The state of the art electromagnetic simulation tool Computer Simulation Technology microwave studio has been used for the design and optimization of the cavity. Different cavity parameters such as the quality factor, shunt impedance, etc. have been estimated with the help of the simulation tool. For the input/output cavities, the issue of symmetric coupling has been studied and a rectangular-shaped central conductor has been proposed to achieve the desired coupling.