In this article we present and design a composite Yb:YAG/YAG asymmetric hexagonal thin disk laser (CAHTDL). At three steps, the absorbed pump distribution by Monte Carlo ray tracing method, the temperature distribution by FEM and finally the output power are calculated. The triplet designing parameters, namely the pump absorption uniformity and efficiency and the temperature distribution are optimized by this model. Our simulation results shows this edge-pumped geometry of disk laser has scaling potential of the solid state lasers up to kW ranges.