Vibratory piling technology does not require analytical tools to predict displacement rates and arising forces. The authors consider the problem of vibratory driving of a pile into a homogeneous unsaturated sandy massif under the action of static and dynamic loads. The purpose of this study is to develop a new analytical solution to the problem of the vibratory pile driving rate in a homogeneous sand base taking vibration creep into account. The solution is provided for the quasi-dynamic problem statement (inertial terms in equations of motion are neglected): the sand medium develops viscous properties due to vibration under the action of the dynamic component of the load, and a pile is driven into the viscous sand base due to the static component of the vertical load. The obtained mathematical model converges with the results of laboratory flume and field experiments performed by other researchers earlier, where the pile vibratory embedding rate increased along with an increase in static loading, the amplitude of dynamic load, and vibration frequency. It can be used to predict the pile or sheet pile driving rate into the unsaturated sand base under the action of vibration, and also to evaluate the necessary parameters of pile driving to obtain the required value of the pile embedding rate.