Pile caps are large structural elements that act as an interface between the superstructure and the pile foundation. The displacement Compatible Strut and Tie Method (C–STM) is an effective nonlinear modelling technique that is mainly used to simulate the behavior of structural reinforced concrete elements having considerable disturbed (D-) regions. Unlike STM, which considers only force equilibrium, C–STM considers displacement compatibility and constitutive material relationships as well. Recently, a three-dimensional (3D) C–STM was formulated and validated for the analysis of four-pile cap specimens of various shapes. In this study, the 3D C–STM is used to predict the complete load-deformation response of three-pile caps under concentric axial loads. The constitutive material relations for concrete and steel used in this study accounts for both concrete softening and tension stiffening. The overall load-deformation behavior simulated using the 3D C–STM agrees well with the experimental data. Moreover, the 3D C–STM also envisages the progression of nonlinear events leading up to the failure of three-pile cap specimen quite well.