To simulate the process of pile installation with a vibratory hammer, this paper presents a theoretical model based on the one-dimensional wave equation and develops a prediction method of the results of the in-situ cone penetration tests (CPT). Computer program is also compiled and verified against an industrial project. Furthermore, the effect of hammer's working frequency, eccentric moment and additional weight are investigated. It shows that, the presented model in this paper simulates the penetration process well for a vibrator driven pile; during installation, the maximum tensile stress in pile shaft is generally smaller than that in compression; the maximum tension stress happens at the end of pile driving. In addition, parameter studies show that increasing the hammer's frequency and eccentric moment improves the hammer's drivability and makes a quicker penetration, e.g. 67% increase in hammer frequency from 30Hz leads to a 170% increase in pile penetration rate, and 50% increase in eccentric moment makes a 240% increase in pile penetration rate; compared with the aforementioned two approaches, a limit positive effect is shown by increasing the additional weight.