Pile supported structures can be subjected to a variety of man-made and naturally occurring dynamic loads. Dynamic loads such as those from rotating machinery include a considerable lateral component. The natural frequency of a pile in the horizontal mode becomes a key parameter in the design of dynamically sensitive equipment foundations. It is not uncommon for structural engineers to estimate the natural frequency of piles using quick linear methods using available soil investigation data before advanced laboratory tests on soil samples can be performed to calibrate nonlinear numerical models. This paper presents results from free and forced vibration tests on a full-scale single pile, designed for a high-speed compressor unit, in Hazira, India. Two different fast mathematical models, one following the Beam on Dynamic Winkler Foundation (BDWF) method, and another involving an FEM–BEM based numerical method were used in predictions against experimental results. The BDWF method was found to produce a preliminary estimate of pile stiffness at low strain levels. However, the selection of soil stiffness and damping models are crucial for the accuracy of BDWF models. It was found that the FEM–BEM model was able to simulate the nonlinear pile response with a moderate overestimation of vibration amplitudes.