Hybrid-type penalty method (HPM) assumes the linear displacement field with rigid displacement, rigid rotation and constant strain in each sub-domain and introduce subsidiary condition about the continuity of displacement into the framework of the variational expression with Lagrange multipliers. This compatibility of the displacement on the intersection boundary is approximately introduced using the penalty as a spring constant which is applied to the Lagrange multiplier. Present method can deal with the fracture on the intersection boundary and yielding in the each element at the same time. This paper shows the upper and lower bound solution for limit analysis using present method.