Load-induced fluid flow acts as a dominant biophysical signal for bone cell mechanotransduction in vivo. Oscillatory fluid flow has been used in bone tissue engineering strategies due to its similarity to the fluid dynamics within the human body. In this study, a fluid-structure interaction method was used to subject the mesenchymal cell to steady and oscillatory fluid flow. Three models were considered for a steady flow, including cytoplasm, nucleus, primary cilium, and cytoskeleton, to investigate the effects of cilium and cytoskeleton on cell mechanical responses (stress and strain). The fourth model, including cytoplasm, primary cilium, and cytoskeleton components has been considered to evaluate the stress and strain values created in the cell and its components in the oscillatory flow regime. The length and mechanical properties of the primary cilium (Young's modulus) were also varied to investigate cell responses. The results indicated that the presence of the cytoskeleton reduced the amount of stress experienced in the cell by about 35%. The presence of primary cilium, also, increased stress in the cell by about ten times in an oscillatory regime. The peak von Mises stress was 11.5 Pa in the oscillatory flow, which is three times greater than the level observed in the steady state condition. Moreover, the highest amount of strain occurred at the base of the cilium, indicating this component's importance in receiving and transmitting stress to other components. Our results revealed a direct relationship between the properties of the cilium and the stress and strain created in the cell. For a cilium with a length of 4 µm, the deflection at the tip of the cilium was 0.77 µm. This represented a 78% increase compared to a 10 µm cilium.  This research can be a basis for future numerical studies in tissue engineering and improvements in the related experimental approaches.