A mathematical model is established for deep-hole(L/D5) boring process

and the system characteristic equation under critical stable conditions is obtained by Lapalace transforming.The frequency response for deep-hole boring process is analyzed by the method of graph.The mechanism of self-shock and the conditions of stability are theoretically studied

and the absolute stable border and the range of damping ratio are pointed out.Combining with the experimental results and practical experiences on boring profound holes

the paper puts forward some specific practical shock absorption and shockproof measures for deep-hole boring process.