Abstract. Scaling laws for hydrodynamically similar implosions are derived by applying the Lie group analysis to the given set of partial differential equations for the hydrodynamic system. Physically this implies that any fluid system belonging to a common similarity group evolves quite in the same manner including hydrodynamic instabilities. The scalings strongly depend on the description of the energy transport mechanism, i.e., whether the fluid system is heat conductive or adiabatic. It has been also found that the property of the hydrodynamically equivalent implosion is most likely kept under a specific condition even when the system is cooperated with such other sources as classical laser absorption, hot electrons, local alpha deposition, and bremsstrahlung loss. The results will give the basis of the target fabrication and diagnostics for the project - fast ignition realization experiments (FIREX : EL = 60 kJ, = 0.35 m, NB = 92 beams).