A numerical simulation of a biperiodic accelerating structure with on-axis coupling cells at a frequency of 2450 MHz for the double-sided cw race-track microtron with an energy of 1.5 GeV now being built at the Institute for Nuclear Physics, Johannes Gutenberg University (Mainz, Germany), was performed. On the basis of these calculations, test cells have been manufactured that are used to develop and refine the methods for measuring and tuning the accelerating structure. The final geometry of cells is established.