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Cytoskeleton is a structure that enables cells to maintain their shape and internal organization. The proper functions of cytoskeleton depend crucially on the mechanical responses and properties of its component filaments (e.g., microtubules and actin filaments). Thus, an in-depth understanding of cytoskeletal filaments mechanics is essential in revealing how cells fulfil their biological functions via cytoskeleton, stimulating the innovative idea in designing biomimetic structure or materials and facilitating to develop novel techniques in disease diagnosis and treatment. This thesis thus focuses on studying the inherent and environmental factors that determine the nanomechanics of cytoskeletal components, i.e., the monomeric feature of cytoskeletal filaments at microscale, the relation between the helical structure and the mechanical properties, and the interaction between the protein filaments and the surrounding environment, such as cytosol, filamentous proteins, electrical fields, etc. The thesis starts with a comprehensive review of the existing cytoskeletal filaments models. It is followed by the molecular structural mechanics models developed for microtubules and actin filaments. Subsequently, the models with monomeric feature were employed to identify the origin of the inter-protofilament sliding and its role in bending and vibration of microtubules. After that, helix structure effects on the mechanics of cytoskeletal filaments were explored. A three-dimensional transverse vibration was reported for microtubules with chiral structures, where the bending axis of the cross-section rotates in an anticlockwise direction and the adjacent half-waves oscillate in different planes. The tension-induced bending was also studied for actin filaments as a result of the helicity. Then, the subcellular environment effect on the filament mechanics was explored. Attempts were also made to reveal the physics of the experimentally observed localized buckling of microtubules and the crucial role of the cross-linker in regulating microtubule stiffness. Also the role of actin-binding proteins in determining the stiffness of actin bundle was examined during the formation of filopodia protrusion. Finally, the studies were carried out for the microtubule vibration excited by the alternating external electric field. Strong correlation was achieved between the tubulin interaction and the frequency shift. Meanwhile, the unique feature of nanoscale microtubule-cytosol interface was studied in detail. Large reduction of the viscous damping of cytosol was achieved in the presence of the nanoscale solid-liquid interface. At the end of the thesis, the contributions of the dissertation research were summarised and remarks were given on future research directions.