A mathematical model and a numerical procedure are presented for analyzing the response of nonuniform piles to vertical vibrations. The methodology presented involves numerical integration of the governing differential equation using a two‐step iteration scheme. The developed model is verified for the case of uniform piles and applied to study the response of tapered piles and two‐component piles. The analyses presented provide some insight into the influence of nonuniform pile geometry on the resonant frequency and amplitude, factors that play a key role in the design of piles subject to vertical vibrations. Owing to its ease of implementation and execution as a computer model, the proposed technique is considered to provide a viable tool for studying the behavior of nonuniform piles for practical applications.