This work analyses the temperature and thermal stress distributions inside Yb:YAG slab crystals with high pump power. The focal lengths of thermal lenses in both thickness and width directions inside the laser crystal are calculated. The hybrid resonator using one-dimensional VRM is designed and the thermal-lensing effects in the slab are considered. The kilo-watts composite Yb:YAG/YAG slab laser pumped by laser diode is presented, in which the corner-pumped scheme is used, with slope efficiency of 43% and optical-to-optical efficiency of 35%. A slab laser scheme with ten kilo-watt output is designed out.