Reactive ion etching process for InGaAs/InP using the CH4/H2 high density inductively coupled plasma was investigated. The experimental design method proposed by Taguchi was utilized to cover the whole parameter range while maintaining reasonable number of actual experiments. Results showed that the ICP power mainly affects surface roughness and verticality of the sidewall, bias power does etch rate and verticality, CH4 gas concentraion does the verticality and etch rate, and the distance between the induction coil and specimen mostly affects the surface roughness. It was also observed that the chamber pressure is the dominant parameter for the etch rate and verticality of the sidewall. The optimum condition was ICP power 700W, bias power 150 W, 15% $CH_4$, 7.5 mTorr, and 14 cm distance, resulting in about 3 $mu extrm{m}$/hr etch rate with smooth surfaces and vertical mesa sidewalls.