Based on the wave theory of the pile-soil system,time domain analysts and frequency domain analysts of pile longitudinal vibration,with a vertical transient impact force applied to the pile top,are studied theoretically. The time-domain velocity curve of integrate pile are fitted with the theoretical curve. The characteristics of time-domain velocity and velocity amplitude spectrum curve of integrate pile are analyzed when pile-soil parameters are changed,similar analysis are studied for non-intact piles( expanding,reducing,segregation). The results shows that the changes have influence on curves,the larger the pile side soil shear wave velocity,the more the pile bottom reflection attenuation. The theoretical response correlates well with the dynamic testing of an engineering pile by the reflected wave method.