The interface hyperbolic model introduced by Clough and Duncan has been most popular among the existing models due to its adaptability in the investigation of soil-structure interaction problems. It is also called as nonlinear elastic hyperbolic interface model. The model is consisting of various input parameters such as interface friction angle (delta), interface adhesion (Ca), interface modulus number (Ki), exponent (n), and failure ratio (Rf). The parameters are determined by laboratory interface shear test using large box shear apparatus. In the literature, the performance of such parameters for varied soil-concrete interfaces has been poorly described. Also the determination of such parameters for every soil-structure interface is a tedious task. As a result, this paper attempts to investigate the effect of moisture content, density, particle size, concrete roughness, normal stress, delta/phi (delta and phi are friction angle for interface and soil, respectively), and Ca/C (Ca is interface adhesion, and C is soil cohesion) on interface hyperbolic model parameters. A total of 64 interface shear tests have been performed on sixteen soil and four rough concrete samples. The results reveal that the particle size and concrete roughness have highest influence on the interface hyperbolic model parameters. Also, this study has explored the appropriate selection of interface reduction factor (delta/phi) and (Ca/C) while analyzing the soil-structure interface.