Ytterbium (Yb) atomic optical clock is currently the most stable optical clock, and its frequency stability has reached 10-19 level. Based on the high-precision Yb atomic optical clock, scientific and applied research in the fields of general relativity testing and geodesy can be carried out. Laser of multiple wavelengths are used in the Yb atomic optical clock, so the frequency control of these lasers is a key technical issue. A four-channel optical ultrastable cavity is carried out, according to the frequency control requirements of four lasers (expect clock laser) in the Yb optical clock system. Then the finite element analysis method is used to obtain the vibration sensitivity and temperature sensitivityof the ultrastable cavity at the best supporting position. The analysis results show that the vertical vibration sensitivity of the optical cavity at the best supporting position is 4.010-9 /g, and the thermal time constant is 53 h. The temperature sensitivity of 1.310-4 is obtained for the ultrastable cavity, when the ambient temperature varies around room temperature, with a period of 24 h and a amplitude of 1 K. These results show that the four-channel ultrastable optical cavity we design can meet the requirements of the frequency stabilization for four lasers (except clock laser) in the Yb optical clock system. The scheme of using simplified four-channel ultrastable cavity for frequency stabilization provides a new technical attempt forthe future miniaturization and integrated design of ytterbium atomic optical clocks.