Purpose: The study proposes a methodology for determining the natural frequencies of vertical vibrations of non-massive bridge supports used in the construction of high-speed railway viaducts. Methods: The article sets out to explore a support model, which is represented by a rod with distributed mass, featuring a concentrated mass at the top. This mass simulates the influence of the superstructure resting on the support. Results: The presented data enable the identification of the support parameters under which the natural frequency of its vertical vibrations can be determined without consideration of the elasticity of the support material and its foundation. Practical significance: Understanding the support parameters that enable the disregard of the elasticity of the support and foundation material enhances the precision of determining the natural frequencies of vertical vibrations. This is of particular importance in the construction of bridge supports, such as viaducts, and other non-massive structures used in the construction of high-speed railways.