Abstract This paper presents the results of a so-called continuum numerical model for wave propagation analysis and soil-pile dynamic response during pile driving. An axisymmetric finite difference numerical model is developed having solid elements for both pile structure and the soil media surrounding and below the pile. Interface elements are used between the pile shaft and the soil to facilitate the sliding between the two media. The performance of the developed model is verified in two stages. First, a simple rod is subjected to a half sine-wave force function at the rod head and the corresponding reflections of force and velocity (multiplied by impedance) are presented for different boundary conditions at the rod tip. The model is then used for signal matching analysis of a real driven pile for which complete information of soil layering, dynamic test signals, and static load test results are available. The signal matching analysis was performed successfully and comparison between several other predicted and measured parameters proved the reasonably good performance of the developed continuum model.