The internal carotid arteries (ICAs) are of vital importance in cerebral blood supply. Hence, accurate modeling of its biomechanical behavior is essential for understanding various pathologies and developing effective treatments. However, computational modeling of the ICA often omits the surrounding tissue environment, which likely limits the accuracy of biomechanical simulations. This study aimed to assess the impact of including surrounding tissues in ICA models on simulation outcomes. Using a single patient-specific ICA geometry, four finite element (FE) models were developed and analyzed: an isolated artery (Model 0), an artery with soft tissue interactions (Model 1), an artery with bone interactions (Model 2), and an artery with both soft tissue and bone interactions (Model 3). The surrounding tissues were modeled using elastic spring elements attached to the outer surface of the arterial wall. Different spring stiffness values were assigned to simulate the distinct properties of surrounding tissues in their corresponding artery segments. Simulations were performed using the FEBio software, the models were analyzed for displacement, stress, and strain distributions. Results showed that surrounding tissues significantly affect arterial biomechanics, with bone having a more dominant effect than soft tissue. The combined tissue model (Model 3) provided the most comprehensive and physiologically accurate representation of the ICA, with a 60.5\% reduction in peak displacement, a 6.8\% reduction in peak stress, and a 33.0\% reduction in peak strain compared to the isolated artery model. However, these preliminary findings using a single ICA geometry prevent us from drawing definitive conclusions. Therefore, our study serves as the groundwork for future investigations and highlights the significance of including surrounding tissues in ICA modeling.