MIRIS is the main payload of the STSAT-3 (Science and Technology Satellite 3) and the first infrared space telescope for astronomical observation in Korea. MIRIS space observation camera (SOC) covers the observation wavelength from $0.9{mu}m$ to $2.0{mu}m$ with a wide field of view $3.67^{circ} imes3.67^{circ}$. The PICNIC HgCdTe detector in a cold box is cooled down below 100K by a micro Stirling cooler of which cooling capacity is 220mW at 77K. MIRIS SOC adopts passive cooling technique to chill the telescope below 200 K by pointing to the deep space (3K). The cooling mechanism employs a radiator, a Winston cone baffle, a thermal shield, MLI (Multi Layer Insulation) of 30 layers, and GFRP (Glass Fiber Reinforced Plastic) pipe support in the system. Optomechanical analysis was made in order to estimate and compensate possible stresses from the thermal contraction of mounting parts at cryogenic temperatures. Finite Element Analysis (FEA) of mechanical structure was also conducted to ensure safety and stability in launching environments and in orbit. MIRIS SOC will mainly perform Galactic plane survey with narrow band filters (Pa $alpha$ and Pa $alpha$ continuum) and CIB (Cosmic Infrared Background) observation with wide band filters (I and H) driven by a cryogenic stepping motor.